Abstract group data - 256.6149

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [8, 4, 4, 4, 8, 4, 8, 8], 'aut_gens': [[1, 8, 32], [193, 252, 176], [195, 140, 48], [83, 124, 224], [215, 188, 224], [83, 172, 160], [211, 92, 240], [135, 248, 48], [65, 252, 160]], 'aut_group': None, 'aut_hash': 1456743208461168318, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 64, 'aut_perms': [33587070022134935264773143873798252440637590450616452406898889658664543348471150100989567, 44698800846734247223526376000140612418335583195468829310943759794462338472321609887508689, 63364774234429487193482839709725039774261125691262652066564706537332472093745504151188689, 124369198932555443752226062005838709223162560502118975018657578382505312332652581783752958, 62609293762152672086224307516457782293441538248666621399500137316958171113941263582170534, 61319206089065455691910757719725466064648113834926961614005911615282248713802311892269440, 78221897152196572672286956926744065991279297979937110187693014927783724694386566768334951, 35569679465768274728753285595967687028822449967426982527158741036971356468123235680416686], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 8, 1], [4, 8, 4, 1], [8, 1, 4, 2], [8, 2, 2, 2], [8, 2, 4, 2], [8, 8, 4, 1], [16, 2, 16, 2], [16, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4.C_2^6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '256.56082', 'autcent_hash': 56082, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '16.11', 'autcentquo_hash': 11, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 1, 4], [4, 2, 10], [4, 8, 4], [8, 1, 8], [8, 2, 12], [8, 8, 4], [16, 2, 32], [16, 8, 8]], 'center_label': '16.5', 'center_order': 16, 'central_product': False, 'central_quotient': '16.11', 'commutator_count': 1, 'commutator_label': '8.2', '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': 6149, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 4], [4, 8, 1, 4], [8, 1, 4, 2], [8, 2, 2, 6], [8, 8, 2, 2], [16, 2, 8, 4], [16, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '32.36', 'frattini_quotient': '8.5', 'hash': 6149, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4], 'inner_gens': [[1, 24, 32], [17, 8, 224], [1, 72, 32]], 'inner_hash': 11, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2\\times D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 56]], 'label': '256.6149', 'linC_count': 768, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 24, 'linQ_dim': 18, 'linQ_dim_count': 8, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4.(C8*Q8)', 'ngens': 3, 'nilpotency_class': 3, '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': 21, 'number_characteristic_subgroups': 41, 'number_conjugacy_classes': 88, 'number_divisions': 34, 'number_normal_subgroups': 83, 'number_subgroup_autclasses': 93, 'number_subgroup_classes': 149, 'number_subgroups': 231, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64], [16, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4, 4], 'outer_gen_pows': [0, 192, 193, 32, 0, 0], 'outer_gens': [[135, 8, 224], [135, 104, 96], [7, 120, 112], [7, 40, 32], [69, 12, 48], [133, 8, 32]], 'outer_group': '256.55647', 'outer_hash': 55647, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 16, 'outer_perms': [127370880, 87091200, 2789705323494, 127371145, 2795972658934, 87119059], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 36, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 8], [8, 2], [16, 4]], 'representations': {'PC': {'code': 641330349680976308293884445295, 'gens': [1, 4, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 16, 41, 786, 771, 91, 1373, 141, 1374, 166]}, 'GLZN': {'d': 2, 'p': 51, 'gens': [3316300, 1724476, 2122432, 132667, 3876, 132664, 5040776, 27030]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [375117, 712973, 115203, 294921, 557073, 573953, 828161, 329062]}, 'Perm': {'d': 36, 'gens': [11909108922970005826033300158761922284765, 22779330023073854372527233838573300338607, 33466694436804376055101725871925988295560, 44107044870068779229997668785772006020576, 54744421048813744680251858160131151045840, 65376838710634752256940001440726428234200, 75424916861104407528393575671021767314640, 44107044870068779229997668785772006020560]}}, 'schur_multiplier': [2, 2], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 2, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4.(C_8\\times Q_8)', 'transitive_degree': 64, '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: 103526590
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 6149, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 103526601
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 6149, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 103526612
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 6149, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 103526623
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 6149, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 144, 'size': 1}
  • id: 103526634
    {'aut_label': '2D', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 6149, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 84, 'size': 2}
  • id: 103526645
    {'aut_label': '2E', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 6149, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 68, 'size': 2}
  • id: 103526656
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 6149, 'group_order': 256, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 4, 'size': 1}
  • id: 103526667
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 6149, 'group_order': 256, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 132, 'size': 1}
  • id: 103526677
    {'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 6149, 'group_order': 256, 'label': '4B1', 'order': 4, 'powers': [2], 'representative': 20, 'size': 1}
  • id: 103526591
    {'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 6149, 'group_order': 256, 'label': '4B-1', 'order': 4, 'powers': [2], 'representative': 148, 'size': 1}
  • id: 103526592
    {'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 6149, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 80, 'size': 2}
  • id: 103526593
    {'aut_label': '4D', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 6149, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 64, 'size': 2}
  • id: 103526594
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 6149, 'group_order': 256, 'label': '4E1', 'order': 4, 'powers': [6], 'representative': 34, 'size': 2}
  • id: 103526595
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 6149, 'group_order': 256, 'label': '4E-1', 'order': 4, 'powers': [6], 'representative': 166, 'size': 2}
  • id: 103526596
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 6149, 'group_order': 256, 'label': '4F1', 'order': 4, 'powers': [6], 'representative': 162, 'size': 2}
  • id: 103526597
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 6149, 'group_order': 256, 'label': '4F-1', 'order': 4, 'powers': [6], 'representative': 38, 'size': 2}
  • id: 103526598
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 6149, 'group_order': 256, 'label': '4G1', 'order': 4, 'powers': [6], 'representative': 50, 'size': 2}
  • id: 103526599
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 6149, 'group_order': 256, 'label': '4G-1', 'order': 4, 'powers': [6], 'representative': 182, 'size': 2}
  • id: 103526600
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 6149, 'group_order': 256, 'label': '4H1', 'order': 4, 'powers': [6], 'representative': 178, 'size': 2}
  • id: 103526602
    {'aut_label': '4E1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 6149, 'group_order': 256, 'label': '4H-1', 'order': 4, 'powers': [6], 'representative': 54, 'size': 2}
  • id: 103526603
    {'aut_label': '4I', 'centralizer': '8.l1.a1', 'counter': 21, 'group_counter': 6149, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [3], 'representative': 8, 'size': 8}
  • id: 103526604
    {'aut_label': '4I', 'centralizer': '8.l1.b1', 'counter': 22, 'group_counter': 6149, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 40, 'size': 8}
  • id: 103526605
    {'aut_label': '4I', 'centralizer': '8.l1.a1', 'counter': 23, 'group_counter': 6149, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [4], 'representative': 12, 'size': 8}
  • id: 103526606
    {'aut_label': '4I', 'centralizer': '8.l1.b1', 'counter': 24, 'group_counter': 6149, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 44, 'size': 8}
  • id: 103526607
    {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 6149, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [7], 'representative': 18, 'size': 1}
  • id: 103526608
    {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 6149, 'group_order': 256, 'label': '8A-1', 'order': 8, 'powers': [8], 'representative': 150, 'size': 1}
  • id: 103526609
    {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 6149, 'group_order': 256, 'label': '8A3', 'order': 8, 'powers': [8], 'representative': 22, 'size': 1}
  • id: 103526610
    {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 6149, 'group_order': 256, 'label': '8A-3', 'order': 8, 'powers': [7], 'representative': 146, 'size': 1}
  • id: 103526611
    {'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 29, 'group_counter': 6149, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [7], 'representative': 2, 'size': 1}
  • id: 103526613
    {'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 30, 'group_counter': 6149, 'group_order': 256, 'label': '8B-1', 'order': 8, 'powers': [8], 'representative': 134, 'size': 1}
  • id: 103526614
    {'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 31, 'group_counter': 6149, 'group_order': 256, 'label': '8B3', 'order': 8, 'powers': [8], 'representative': 6, 'size': 1}
  • id: 103526615
    {'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 32, 'group_counter': 6149, 'group_order': 256, 'label': '8B-3', 'order': 8, 'powers': [7], 'representative': 130, 'size': 1}
  • id: 103526616
    {'aut_label': '8C1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 6149, 'group_order': 256, 'label': '8C1', 'order': 8, 'powers': [12], 'representative': 32, 'size': 2}
  • id: 103526617
    {'aut_label': '8C1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 6149, 'group_order': 256, 'label': '8C3', 'order': 8, 'powers': [12], 'representative': 160, 'size': 2}
  • id: 103526618
    {'aut_label': '8C1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 6149, 'group_order': 256, 'label': '8D1', 'order': 8, 'powers': [12], 'representative': 48, 'size': 2}
  • id: 103526619
    {'aut_label': '8C1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 6149, 'group_order': 256, 'label': '8D3', 'order': 8, 'powers': [12], 'representative': 176, 'size': 2}
  • id: 103526620
    {'aut_label': '8E1', 'centralizer': '2.b1.a1', 'counter': 37, 'group_counter': 6149, 'group_order': 256, 'label': '8E1', 'order': 8, 'powers': [12], 'representative': 36, 'size': 2}
  • id: 103526621
    {'aut_label': '8E1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 6149, 'group_order': 256, 'label': '8E-1', 'order': 8, 'powers': [12], 'representative': 164, 'size': 2}
  • id: 103526622
    {'aut_label': '8E1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 6149, 'group_order': 256, 'label': '8F1', 'order': 8, 'powers': [12], 'representative': 52, 'size': 2}
  • id: 103526624
    {'aut_label': '8E1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 6149, 'group_order': 256, 'label': '8F-1', 'order': 8, 'powers': [12], 'representative': 180, 'size': 2}
  • id: 103526625
    {'aut_label': '8G1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 6149, 'group_order': 256, 'label': '8G1', 'order': 8, 'powers': [8], 'representative': 82, 'size': 2}
  • id: 103526626
    {'aut_label': '8G1', 'centralizer': '2.b1.a1', 'counter': 42, 'group_counter': 6149, 'group_order': 256, 'label': '8G-1', 'order': 8, 'powers': [7], 'representative': 86, 'size': 2}
  • id: 103526627
    {'aut_label': '8H1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 6149, 'group_order': 256, 'label': '8H1', 'order': 8, 'powers': [8], 'representative': 66, 'size': 2}
  • id: 103526628
    {'aut_label': '8H1', 'centralizer': '2.b1.a1', 'counter': 44, 'group_counter': 6149, 'group_order': 256, 'label': '8H-1', 'order': 8, 'powers': [7], 'representative': 70, 'size': 2}
  • id: 103526629
    {'aut_label': '8I1', 'centralizer': '8.l1.a1', 'counter': 45, 'group_counter': 6149, 'group_order': 256, 'label': '8I1', 'order': 8, 'powers': [9], 'representative': 10, 'size': 8}
  • id: 103526630
    {'aut_label': '8I1', 'centralizer': '8.l1.a1', 'counter': 46, 'group_counter': 6149, 'group_order': 256, 'label': '8I-1', 'order': 8, 'powers': [10], 'representative': 14, 'size': 8}
  • id: 103526631
    {'aut_label': '8I1', 'centralizer': '8.l1.b1', 'counter': 47, 'group_counter': 6149, 'group_order': 256, 'label': '8J1', 'order': 8, 'powers': [9], 'representative': 42, 'size': 8}
  • id: 103526632
    {'aut_label': '8I1', 'centralizer': '8.l1.b1', 'counter': 48, 'group_counter': 6149, 'group_order': 256, 'label': '8J-1', 'order': 8, 'powers': [10], 'representative': 46, 'size': 8}
  • id: 103526633
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 49, 'group_counter': 6149, 'group_order': 256, 'label': '16A1', 'order': 16, 'powers': [29], 'representative': 1, 'size': 2}
  • id: 103526635
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 50, 'group_counter': 6149, 'group_order': 256, 'label': '16A-1', 'order': 16, 'powers': [30], 'representative': 135, 'size': 2}
  • id: 103526636
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 51, 'group_counter': 6149, 'group_order': 256, 'label': '16A3', 'order': 16, 'powers': [31], 'representative': 3, 'size': 2}
  • id: 103526637
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 52, 'group_counter': 6149, 'group_order': 256, 'label': '16A-3', 'order': 16, 'powers': [32], 'representative': 133, 'size': 2}
  • id: 103526638
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 53, 'group_counter': 6149, 'group_order': 256, 'label': '16A5', 'order': 16, 'powers': [32], 'representative': 5, 'size': 2}
  • id: 103526639
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 54, 'group_counter': 6149, 'group_order': 256, 'label': '16A-5', 'order': 16, 'powers': [31], 'representative': 131, 'size': 2}
  • id: 103526640
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 55, 'group_counter': 6149, 'group_order': 256, 'label': '16A7', 'order': 16, 'powers': [30], 'representative': 7, 'size': 2}
  • id: 103526641
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 6149, 'group_order': 256, 'label': '16A-7', 'order': 16, 'powers': [29], 'representative': 129, 'size': 2}
  • id: 103526642
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 6149, 'group_order': 256, 'label': '16B1', 'order': 16, 'powers': [32], 'representative': 65, 'size': 2}
  • id: 103526643
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 6149, 'group_order': 256, 'label': '16B-1', 'order': 16, 'powers': [31], 'representative': 71, 'size': 2}
  • id: 103526644
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 6149, 'group_order': 256, 'label': '16B3', 'order': 16, 'powers': [30], 'representative': 195, 'size': 2}
  • id: 103526646
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 60, 'group_counter': 6149, 'group_order': 256, 'label': '16B-3', 'order': 16, 'powers': [29], 'representative': 197, 'size': 2}
  • id: 103526647
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 6149, 'group_order': 256, 'label': '16B5', 'order': 16, 'powers': [29], 'representative': 69, 'size': 2}
  • id: 103526648
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 6149, 'group_order': 256, 'label': '16B-5', 'order': 16, 'powers': [30], 'representative': 67, 'size': 2}
  • id: 103526649
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 63, 'group_counter': 6149, 'group_order': 256, 'label': '16B7', 'order': 16, 'powers': [31], 'representative': 199, 'size': 2}
  • id: 103526650
    {'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 64, 'group_counter': 6149, 'group_order': 256, 'label': '16B-7', 'order': 16, 'powers': [32], 'representative': 193, 'size': 2}
  • id: 103526651
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 65, 'group_counter': 6149, 'group_order': 256, 'label': '16C1', 'order': 16, 'powers': [43], 'representative': 33, 'size': 2}
  • id: 103526652
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 66, 'group_counter': 6149, 'group_order': 256, 'label': '16C-1', 'order': 16, 'powers': [44], 'representative': 103, 'size': 2}
  • id: 103526653
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 67, 'group_counter': 6149, 'group_order': 256, 'label': '16C3', 'order': 16, 'powers': [44], 'representative': 99, 'size': 2}
  • id: 103526654
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 68, 'group_counter': 6149, 'group_order': 256, 'label': '16C-3', 'order': 16, 'powers': [43], 'representative': 37, 'size': 2}
  • id: 103526655
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 69, 'group_counter': 6149, 'group_order': 256, 'label': '16C5', 'order': 16, 'powers': [43], 'representative': 165, 'size': 2}
  • id: 103526657
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 70, 'group_counter': 6149, 'group_order': 256, 'label': '16C-5', 'order': 16, 'powers': [44], 'representative': 51, 'size': 2}
  • id: 103526658
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 71, 'group_counter': 6149, 'group_order': 256, 'label': '16C7', 'order': 16, 'powers': [44], 'representative': 55, 'size': 2}
  • id: 103526659
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 72, 'group_counter': 6149, 'group_order': 256, 'label': '16C-7', 'order': 16, 'powers': [43], 'representative': 161, 'size': 2}
  • id: 103526660
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 73, 'group_counter': 6149, 'group_order': 256, 'label': '16D1', 'order': 16, 'powers': [43], 'representative': 97, 'size': 2}
  • id: 103526661
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 74, 'group_counter': 6149, 'group_order': 256, 'label': '16D-1', 'order': 16, 'powers': [44], 'representative': 39, 'size': 2}
  • id: 103526662
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 75, 'group_counter': 6149, 'group_order': 256, 'label': '16D3', 'order': 16, 'powers': [44], 'representative': 35, 'size': 2}
  • id: 103526663
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 76, 'group_counter': 6149, 'group_order': 256, 'label': '16D-3', 'order': 16, 'powers': [43], 'representative': 101, 'size': 2}
  • id: 103526664
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 77, 'group_counter': 6149, 'group_order': 256, 'label': '16D5', 'order': 16, 'powers': [43], 'representative': 53, 'size': 2}
  • id: 103526665
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 78, 'group_counter': 6149, 'group_order': 256, 'label': '16D-5', 'order': 16, 'powers': [44], 'representative': 163, 'size': 2}
  • id: 103526666
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 79, 'group_counter': 6149, 'group_order': 256, 'label': '16D7', 'order': 16, 'powers': [44], 'representative': 167, 'size': 2}
  • id: 103526668
    {'aut_label': '16C1', 'centralizer': '2.b1.a1', 'counter': 80, 'group_counter': 6149, 'group_order': 256, 'label': '16D-7', 'order': 16, 'powers': [43], 'representative': 49, 'size': 2}
  • id: 103526669
    {'aut_label': '16E1', 'centralizer': '8.n1.a1', 'counter': 81, 'group_counter': 6149, 'group_order': 256, 'label': '16E1', 'order': 16, 'powers': [29], 'representative': 9, 'size': 8}
  • id: 103526670
    {'aut_label': '16E1', 'centralizer': '8.n1.a1', 'counter': 82, 'group_counter': 6149, 'group_order': 256, 'label': '16E-1', 'order': 16, 'powers': [30], 'representative': 15, 'size': 8}
  • id: 103526671
    {'aut_label': '16E1', 'centralizer': '8.n1.a1', 'counter': 83, 'group_counter': 6149, 'group_order': 256, 'label': '16E3', 'order': 16, 'powers': [31], 'representative': 11, 'size': 8}
  • id: 103526672
    {'aut_label': '16E1', 'centralizer': '8.n1.a1', 'counter': 84, 'group_counter': 6149, 'group_order': 256, 'label': '16E-3', 'order': 16, 'powers': [32], 'representative': 13, 'size': 8}
  • id: 103526673
    {'aut_label': '16E1', 'centralizer': '8.n1.b1', 'counter': 85, 'group_counter': 6149, 'group_order': 256, 'label': '16F1', 'order': 16, 'powers': [29], 'representative': 41, 'size': 8}
  • id: 103526674
    {'aut_label': '16E1', 'centralizer': '8.n1.b1', 'counter': 86, 'group_counter': 6149, 'group_order': 256, 'label': '16F-1', 'order': 16, 'powers': [30], 'representative': 47, 'size': 8}
  • id: 103526675
    {'aut_label': '16E1', 'centralizer': '8.n1.b1', 'counter': 87, 'group_counter': 6149, 'group_order': 256, 'label': '16F3', 'order': 16, 'powers': [31], 'representative': 43, 'size': 8}
  • id: 103526676
    {'aut_label': '16E1', 'centralizer': '8.n1.b1', 'counter': 88, 'group_counter': 6149, 'group_order': 256, 'label': '16F-3', 'order': 16, 'powers': [32], 'representative': 45, 'size': 8}
• gps_qchar •

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

  
  
  • id: 2322012
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2322023
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 2322034
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 2322040
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 2322041
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 2322042
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2322043
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2322044
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2322045
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322013
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322014
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322015
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322020
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322021
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322022
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, -2, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322024
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 2, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322025
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2e', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2322026
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2f', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2322027
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2g', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 0, 0, -2, -2, -2, 0, 2, 0, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2322028
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2h', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 0, 0, 2, 2, 2, 0, -2, 0, -2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 2322016
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322017
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1n', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322018
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1o', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322019
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.1p', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322029
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2i', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322030
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2j', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322031
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2k', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, -4, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322032
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2l', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 4, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322033
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2m', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, -8, 8, 8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322035
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2n', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, -8, -8, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322036
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2o', 'multiplicity': 8, 'nt': [32, 1951], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, -8, 8, 8, 0, 8, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322037
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2p', 'multiplicity': 8, 'nt': [32, 1951], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 8, -8, -8, 0, -8, 8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322038
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2q', 'multiplicity': 8, 'nt': [32, 1951], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, -8, 8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2322039
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '256.6149', 'group_order': 256, 'image': None, 'label': '256.6149.2r', 'multiplicity': 8, 'nt': [32, 1951], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, 8, -8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 2932688
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.6149.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 2932699
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 128, 'label': '256.6149.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 2932710
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.b1', 'kernel_order': 128, 'label': '256.6149.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 2932721
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.6149.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 2932732
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.6149.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 2932743
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.6149.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 2932754
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.6149.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 2932765
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.6149.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 2932775
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1.a1', 'kernel_order': 64, 'label': '256.6149.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 2932689
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  • id: 2932690
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 64, 'label': '256.6149.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 2932691
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 64, 'label': '256.6149.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 2932692
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  • id: 2932693
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  • id: 2932694
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  • id: 2932695
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  • id: 2932696
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  • id: 2932697
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  • id: 2932698
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  • id: 2932700
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  • id: 2932701
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  • id: 2932702
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  • id: 2932703
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  • id: 2932704
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  • id: 2932705
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 25, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.h1.b1', 'kernel_order': 32, 'label': '256.6149.1o1', 'nt': [8, 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, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]]]}
  • id: 2932706
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 26, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.h1.b1', 'kernel_order': 32, 'label': '256.6149.1o2', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]]]}
  • id: 2932707
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 27, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.h1.b1', 'kernel_order': 32, 'label': '256.6149.1o3', 'nt': [8, 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, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]]]}
  • id: 2932708
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 28, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.h1.b1', 'kernel_order': 32, 'label': '256.6149.1o4', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]]]}
  • id: 2932709
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.g1.b1', 'kernel_order': 32, 'label': '256.6149.1p1', 'nt': [8, 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, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
  • id: 2932711
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.g1.b1', 'kernel_order': 32, 'label': '256.6149.1p2', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
  • id: 2932712
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.g1.b1', 'kernel_order': 32, 'label': '256.6149.1p3', 'nt': [8, 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, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
  • id: 2932713
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.g1.b1', 'kernel_order': 32, 'label': '256.6149.1p4', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
  • id: 2932714
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.k1.a1', 'kernel_order': 32, 'label': '256.6149.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932715
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.k1.b1', 'kernel_order': 32, 'label': '256.6149.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932716
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  • id: 2932717
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  • id: 2932718
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  • id: 2932719
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  • id: 2932720
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  • id: 2932722
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 40, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.i1.a1', 'kernel_order': 32, 'label': '256.6149.2h', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932723
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 41, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.b1', 'kernel_order': 16, 'label': '256.6149.2i1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932724
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 42, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.b1', 'kernel_order': 16, 'label': '256.6149.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932725
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 43, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.a1', 'kernel_order': 16, 'label': '256.6149.2j1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932726
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 44, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.a1', 'kernel_order': 16, 'label': '256.6149.2j2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2932727
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 45, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.a1', 'kernel_order': 16, 'label': '256.6149.2k1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932728
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  • id: 2932729
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 47, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 16, 'label': '256.6149.2l1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932730
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 48, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 16, 'label': '256.6149.2l2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932731
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 49, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.g1.a1', 'kernel_order': 8, 'label': '256.6149.2m1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 1]], [[0, 0]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 3]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932733
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 50, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.g1.a1', 'kernel_order': 8, 'label': '256.6149.2m2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 3]], [[0, 0]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 3]], [[-2, 3]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932734
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 51, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.g1.a1', 'kernel_order': 8, 'label': '256.6149.2m3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[0, 0]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 3]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932735
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 52, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.g1.a1', 'kernel_order': 8, 'label': '256.6149.2m4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[0, 0]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 3]], [[2, 3]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932736
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 53, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.6149.2n1', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932737
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 54, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.6149.2n2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 3]], [[-2, 3]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932738
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 55, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.6149.2n3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932739
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 56, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.6149.2n4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 1]], [[2, 3]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932740
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  • id: 2932741
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 58, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o2', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-2, 3]], [[-2, 1]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[2, 7]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[2, 1]], [[-1, 1], [1, 5]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[2, 5]], [[0, 0]], [[2, 3]], [[0, 0]], [[-1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932742
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 59, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o3', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-2, 5]], [[-2, 7]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[2, 1]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[2, 7]], [[1, 3], [-1, 7]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[2, 3]], [[0, 0]], [[2, 5]], [[0, 0]], [[1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932744
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 60, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o4', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[2, 3]], [[2, 1]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[-2, 7]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[-2, 1]], [[1, 1], [-1, 5]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[-2, 5]], [[0, 0]], [[-2, 3]], [[0, 0]], [[1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932745
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 61, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o5', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[2, 1]], [[-2, 3]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[2, 5]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[2, 3]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[-2, 7]], [[0, 0]], [[-2, 1]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932746
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 62, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o6', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-2, 7]], [[2, 5]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[-2, 3]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-1, 7]], [[-2, 5]], [[1, 1], [1, 5]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[2, 1]], [[0, 0]], [[2, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932747
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 63, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o7', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[-2, 1]], [[2, 3]], [[0, 0]], [[2, 5]], [[0, 0]], [[-2, 7]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[-2, 5]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[-2, 3]], [[1, 3], [1, 7]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[2, 7]], [[0, 0]], [[2, 1]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932748
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 64, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2o8', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[2, 7]], [[-2, 5]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[2, 3]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[2, 5]], [[-1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[-2, 1]], [[0, 0]], [[-2, 7]], [[0, 0]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932749
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 65, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p1', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[-2, 5]], [[-2, 7]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[2, 1]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 3], [-1, 7]], [[0, 0]], [[1, 1], [1, 5]], [[2, 7]], [[-1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[2, 3]], [[0, 0]], [[2, 5]], [[0, 0]], [[-1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932750
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 66, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p2', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[2, 3]], [[2, 1]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[-2, 7]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[-2, 1]], [[-1, 1], [1, 5]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[-2, 5]], [[0, 0]], [[-2, 3]], [[0, 0]], [[-1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932751
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 67, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p3', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[2, 5]], [[2, 7]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[-2, 1]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[-2, 7]], [[1, 3], [-1, 7]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[-2, 3]], [[0, 0]], [[-2, 5]], [[0, 0]], [[1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932752
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 68, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p4', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-2, 3]], [[-2, 1]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[2, 7]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[2, 1]], [[1, 1], [-1, 5]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[2, 5]], [[0, 0]], [[2, 3]], [[0, 0]], [[1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932753
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 69, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p5', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-2, 1]], [[2, 3]], [[0, 0]], [[2, 5]], [[0, 0]], [[-2, 7]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[-2, 5]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-2, 3]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[2, 7]], [[0, 0]], [[2, 1]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932755
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 70, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p6', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[2, 7]], [[-2, 5]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[2, 3]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-1, 7]], [[2, 5]], [[1, 1], [1, 5]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[-2, 1]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932756
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 71, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p7', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[2, 1]], [[-2, 3]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[2, 5]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[2, 3]], [[1, 3], [1, 7]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[-2, 7]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932757
    {'center': '8.f1.b1', 'center_index': 8, 'center_order': 32, 'counter': 72, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.6149.2p8', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 4]], [[2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[-2, 7]], [[2, 5]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[-2, 3]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[-2, 5]], [[-1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[2, 1]], [[0, 0]], [[2, 7]], [[0, 0]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932758
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  • id: 2932759
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 74, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q2', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-2, 5]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[2, 3]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 1], [-1, 5]], [[-2, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[1, 3], [-1, 7]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932760
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 75, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q3', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[-2, 3]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[2, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 3], [1, 7]], [[-2, 1]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[-1, 1], [1, 5]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932761
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 76, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q4', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[2, 5]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[-2, 3]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[2, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[-1, 3], [1, 7]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932762
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 77, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q5', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[2, 7]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[2, 5]], [[0, 0]], [[-2, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[-2, 1]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[-2, 5]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[-1, 1], [-1, 5]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932763
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 78, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q6', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [1, 5]], [[-2, 1]], [[-1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[2, 7]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]], [[2, 3]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[1, 3], [1, 7]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932764
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 79, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q7', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-2, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[2, 1]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[2, 5]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[1, 1], [1, 5]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932766
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 80, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2q8', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[2, 1]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[-2, 7]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]], [[-2, 3]], [[1, 3], [-1, 7]], [[0, 0]], [[1, 1], [1, 5]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[-1, 3], [-1, 7]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932767
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 81, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r1', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [1, 7]], [[-2, 3]], [[-1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[-1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[2, 5]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 3], [-1, 7]], [[-2, 1]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[1, 1], [-1, 5]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932768
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 82, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r2', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[2, 5]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[1, 1], [1, 5]], [[-2, 3]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[1, 1], [-1, 5]], [[2, 7]], [[1, 3], [1, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[1, 3], [-1, 7]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932769
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 83, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r3', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[2, 3]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[1, 3], [1, 7]], [[-2, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 3], [1, 7]], [[2, 1]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[2, 5]], [[0, 0]], [[-2, 7]], [[-1, 1], [1, 5]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932770
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 84, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r4', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-2, 5]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[-1, 1], [-1, 5]], [[2, 3]], [[0, 0]], [[1, 3], [1, 7]], [[1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[-2, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 1], [1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[-1, 3], [1, 7]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932771
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 85, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r5', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 5]], [[-1, 3], [1, 7]], [[-2, 7]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[-2, 5]], [[0, 0]], [[2, 7]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 1], [1, 5]], [[1, 3], [-1, 7]], [[2, 1]], [[0, 0]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[2, 5]], [[-1, 1], [1, 5]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[-1, 1], [-1, 5]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932772
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 86, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r6', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [1, 5]], [[2, 1]], [[-1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[-2, 7]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]], [[-2, 3]], [[-1, 3], [1, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[2, 5]], [[1, 3], [1, 7]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932773
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 87, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r7', 'nt': [32, 1951], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[-2, 4]], [[2, 4]], [[2, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[1, 0], [-1, 4]], [[0, 0]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[-2, 6]], [[2, 2]], [[-2, 2]], [[2, 6]], [[2, 6]], [[-2, 2]], [[2, 2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 6]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 5]], [[1, 3], [-1, 7]], [[2, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[2, 5]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[-1, 3], [1, 7]], [[-2, 1]], [[0, 0]], [[-1, 1], [1, 5]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[-2, 5]], [[1, 1], [-1, 5]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [-1, 7]], [[1, 1], [1, 5]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 3]], [[1, 1], [1, 5]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2932774
    {'center': '8.f1.a1', 'center_index': 8, 'center_order': 32, 'counter': 88, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.6149', 'group_counter': 6149, 'group_order': 256, 'image': None, 'image_isoclass': '128.902', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.6149.2r8', 'nt': [32, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[2, 4]], [[-2, 4]], [[-2, 4]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[1, 0], [1, 4]], [[0, 0]], [[1, 0], [-1, 4]], [[-1, 0], [-1, 4]], [[-1, 0], [1, 4]], [[1, 0], [1, 4]], [[-1, 0], [1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 2]], [[-2, 6]], [[2, 6]], [[-2, 2]], [[-2, 2]], [[2, 6]], [[-2, 6]], [[1, 2], [1, 6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, 6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 7]], [[1, 1], [-1, 5]], [[-2, 1]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 3], [1, 7]], [[-1, 1], [1, 5]], [[2, 7]], [[0, 0]], [[-1, 3], [1, 7]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]], [[2, 3]], [[1, 3], [-1, 7]], [[0, 0]], [[1, 1], [1, 5]], [[1, 1], [-1, 5]], [[-1, 3], [-1, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[-2, 5]], [[-1, 3], [-1, 7]], [[2, 5]], [[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: 50399349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.6149.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.6149', 'subgroup_hash': 6149, 'subgroup_order': 256, 'subgroup_tex': 'C_4.(C_8\\times Q_8)', 'supersolvable': True, 'sylow': 2}
  • id: 50399410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.504', 'subgroup_hash': 504, 'subgroup_order': 128, 'subgroup_tex': 'C_8.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 50399421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.837', 'subgroup_hash': 837, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\times C_4\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.884', 'subgroup_hash': 884, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.883', 'subgroup_hash': 883, 'subgroup_order': 128, 'subgroup_tex': 'C_8.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 50399454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.883', 'subgroup_hash': 883, 'subgroup_order': 128, 'subgroup_tex': 'C_8.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 50399465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.111', 'subgroup_hash': 111, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{32}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.2.e1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.111', 'subgroup_hash': 111, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{32}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, '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': '64.83', 'subgroup_hash': 83, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, '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': '64.86', 'subgroup_hash': 86, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, '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': '64.86', 'subgroup_hash': 86, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.108', 'subgroup_hash': 108, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, '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': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.183', 'subgroup_hash': 183, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, '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': '64.183', 'subgroup_hash': 183, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, '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': '64.184', 'subgroup_hash': 184, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.b1', 'outer_equivalence': False, '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': '64.184', 'subgroup_hash': 184, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.110', 'subgroup_hash': 110, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.44', 'subgroup_hash': 44, 'subgroup_order': 64, 'subgroup_tex': 'C_4:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.44', 'subgroup_hash': 44, 'subgroup_order': 64, 'subgroup_tex': 'C_4:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.44', 'subgroup_hash': 44, 'subgroup_order': 64, 'subgroup_tex': 'C_4:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.44', 'subgroup_hash': 44, 'subgroup_order': 64, 'subgroup_tex': 'C_4:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.26', 'subgroup_hash': 26, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.26', 'subgroup_hash': 26, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399419
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 50399420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, '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': ['Phi', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.b1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.8.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 50399458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, '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': ['Z', 'U2'], 'split': False, '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: 50399460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_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: 50399473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_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: 50399474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.a1', 'outer_equivalence': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 50399479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.16.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399492
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399493
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399494
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399495
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399496
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399497
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.16.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 50399351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}: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: 50399352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 50399353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.36', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], '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: 50399354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times Q_8', '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: 50399355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\OD_{16}', '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: 50399356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.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: 50399357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}: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: 50399358
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 107, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.35', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399359
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 108, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399360
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 109, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399362
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 110, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399363
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399364
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399365
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.32.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 50399367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399374
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399375
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.32.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.32.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.115', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 115, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 50399381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.127', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 127, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 50399382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.6149.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.105', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 105, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 50399384
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 130, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.70', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 70, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 50399385
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 131, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.117', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 117, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_4', '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: 50399386
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 132, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.126', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 126, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8\\times Q_8', '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: 50399387
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 133, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.103', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 103, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_4', '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: 50399388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.6149.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399392
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399393
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399395
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399398
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.64.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399399
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 144, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.671', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 671, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', '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: 50399400
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.902', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 902, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 50399401
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.6149.128.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.902', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 902, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 50399402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399403
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.6149.128.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 50399404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.6149', 'ambient_counter': 6149, 'ambient_order': 256, 'ambient_tex': 'C_4.(C_8\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 149, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.6149.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.6149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6149, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.(C_8\\times Q_8)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 50399349
    {'ambient': '256.6149', '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': '16.b1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.e1.a1', '2.e1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4050, 6534, 3203, 6870, 4096, 6522, 3211, 6783], 'generators': [1, 8, 32], 'label': '256.6149.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.e1.a1', '2.e1.b1', '2.d1.a1', '2.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399350
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.b1', '8.e1.a1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7190, 3584, 7015, 2660, 7277, 3590, 7002, 2626], 'generators': [10, 34], 'label': '256.6149.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399351
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.h1.a1', '64.h1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6328, 3607, 8464, 4741, 6399, 3585, 8484, 4681], 'generators': [16, 196, 128], 'label': '256.6149.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '64.c1.a1', '64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '64.115', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399352
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.p1.a1', '16.p1.b1', '16.q1.a1', '16.q1.b1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.e1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5987, 5883, 5511, 6218, 6054, 5846, 5524, 6190], 'generators': [16, 4], 'label': '256.6149.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '64.d1.a1', '64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '32.25', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.25', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399353
    {'ambient': '256.6149', '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': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.d1.c1', '16.d1.d1', '16.e1.a1', '16.f1.a1'], 'contains': ['64.a1.a1', '64.f1.a1', '64.g1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8193, 1714, 7299, 2049, 8285, 1703, 7317, 2051], 'generators': [16, 192], 'label': '256.6149.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.d1.c1', '16.d1.d1', '16.f1.a1', '16.e1.a1'], 'normal_contains': ['64.a1.a1', '64.f1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.115', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399354
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.d1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.g1.a1', '16.h1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.f1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4712, 6696, 3960, 5701, 4765, 6653, 3887, 5679], 'generators': [208, 4], 'label': '256.6149.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.a1.a1', '16.h1.a1', '16.g1.a1'], 'normal_contains': ['64.b1.a1', '64.d1.a1', '64.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.2', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399355
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.e1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.i1.a1', '16.i1.b1', '16.r1.a1', '16.r1.b1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.g1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7318, 2957, 6645, 3828, 7400, 2938, 6661, 3752], 'generators': [20, 192], 'label': '256.6149.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.a1.a1', '16.i1.a1', '16.i1.b1'], 'normal_contains': ['64.b1.a1', '64.e1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.117', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399356
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.f1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.j1.b1', '16.k1.a1', '16.l1.a1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.g1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5137, 5071, 4802, 5201, 5195, 5039, 4815, 5136], 'generators': [192, 4], 'label': '256.6149.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.a1.a1', '16.j1.a1', '16.j1.b1', '16.l1.a1', '16.k1.a1', '16.m1.b1', '16.m1.a1'], 'normal_contains': ['64.c1.a1', '64.d1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399357
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.g1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.s1.a1', '16.t1.a1', '16.t1.b1'], 'contains': ['64.c1.a1', '64.e1.a1', '64.f1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6668, 4259, 7057, 4350, 6743, 4231, 7074, 4295], 'generators': [20, 196], 'label': '256.6149.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.c1.a1', '64.e1.a1', '64.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.117', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399358
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.h1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.g1.a1', '16.k1.a1'], 'contains': ['64.d1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3472, 8721, 3728, 7725, 3511, 8665, 3672, 7638], 'generators': [18], 'label': '256.6149.32.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': ['16.b1.a1', '16.k1.a1', '16.g1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '32.35', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.35', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399359
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.h1.a1', '16.l1.a1', '16.u1.a1', '16.u1.b1', '16.v1.a1', '16.v1.b1'], 'contains': ['64.d1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2370, 8177, 3011, 6607, 2396, 8125, 3018, 6573], 'generators': [2], 'label': '256.6149.32.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': ['16.b1.a1', '16.l1.a1', '16.h1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.i1.a1', 'projective_image': '32.28', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.28', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399360
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.j1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.h1.a1', '16.k1.a1'], 'contains': ['64.d1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3963, 7748, 4145, 6873, 4007, 7697, 4073, 6836], 'generators': [210], 'label': '256.6149.32.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1.a1', 'normal_contained_in': ['16.c1.a1', '16.k1.a1', '16.h1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.2', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399361
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.d1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.k1.b1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5085, 5932, 4482, 6028, 5141, 5923, 4459, 5952], 'generators': [32, 2, 16], 'label': '256.6149.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.d1.a1', '8.k1.a1', '8.k1.b1', '8.j1.a1', '8.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399362
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '32.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.g1.a1', '16.l1.a1', '16.w1.a1', '16.w1.b1'], 'contains': ['64.d1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3738, 7317, 2406, 7280, 3780, 7270, 2344, 7208], 'generators': [194], 'label': '256.6149.32.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': ['16.c1.a1', '16.l1.a1', '16.g1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399363
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.i1.a1', '16.m1.a1'], 'contains': ['64.g1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7868, 2335, 5753, 3393, 7956, 2320, 5767, 3350], 'generators': [32], 'label': '256.6149.32.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': ['16.e1.a1', '16.m1.a1', '16.i1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.l1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399364
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.i1.b1', '16.m1.b1'], 'contains': ['64.g1.a1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7868, 2335, 6196, 2876, 7956, 2320, 6182, 2839], 'generators': [48], 'label': '256.6149.32.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': ['16.e1.a1', '16.m1.b1', '16.i1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.l1.b1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399365
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '32.m1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.i1.b1', '16.m1.a1'], 'contains': ['64.g1.a1'], 'core': '32.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7642, 1093, 5939, 3134, 7729, 1086, 5925, 3095], 'generators': [36], 'label': '256.6149.32.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.m1.a1', 'normal_contained_in': ['16.f1.a1', '16.m1.a1', '16.i1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.m1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399366
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '32.m1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.i1.a1', '16.m1.b1'], 'contains': ['64.g1.a1'], 'core': '32.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7642, 1093, 6067, 2617, 7729, 1086, 6053, 2584], 'generators': [52], 'label': '256.6149.32.m1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.m1.b1', 'normal_contained_in': ['16.f1.a1', '16.m1.b1', '16.i1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.m1.b1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399367
    {'ambient': '256.6149', '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': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.o1.a1', '16.p1.a1'], 'contains': ['64.a1.a1', '64.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8617, -1, 8027, -1, 8714, -1, 8046, -1], 'generators': [8, 128], 'label': '256.6149.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.n1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399368
    {'ambient': '256.6149', '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': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.o1.b1', '16.p1.b1'], 'contains': ['64.a1.a1', '64.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8617, -1, 7784, -1, 8714, -1, 7803, -1], 'generators': [40, 128], 'label': '256.6149.32.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '32.n1.b1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399369
    {'ambient': '256.6149', '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': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.c1', '16.o1.a1', '16.p1.a1'], 'contains': ['64.a1.a1', '64.i1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8617, -1, 8270, -1, 8714, -1, 8289, -1], 'generators': [12, 128], 'label': '256.6149.32.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.n1.c1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399370
    {'ambient': '256.6149', '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': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.d1', '16.o1.b1', '16.p1.b1'], 'contains': ['64.a1.a1', '64.i1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8617, -1, 7542, -1, 8714, -1, 7560, -1], 'generators': [44, 128], 'label': '256.6149.32.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '32.n1.d1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399371
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.n1.a1', '16.s1.a1'], 'contains': ['64.c1.a1', '64.j1.a1', '64.j1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 8901, -1, 5625, -1, 8922, -1], 'generators': [34, 128], 'label': '256.6149.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.o1.a1', 'projective_image': '128.671', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399372
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2323', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.e1.a1', '8.l1.a1', '8.m1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6459, 4707, 5696, 4579, 6418, 4706, 5710, 4522], 'generators': [8, 2, 192], 'label': '256.6149.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.e1.a1', '2.d1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399373
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.n1.a1', '16.s1.a1'], 'contains': ['64.c1.a1', '64.j1.c1', '64.j1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 8658, -1, 5625, -1, 8679, -1], 'generators': [50, 128], 'label': '256.6149.32.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.o1.b1', 'projective_image': '128.671', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399374
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.r1.a1', '16.t1.a1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6993, -1, 6379, -1, 7072, -1, 6393, -1], 'generators': [10], 'label': '256.6149.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.p1.a1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399375
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.r1.b1', '16.t1.b1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6993, -1, 6830, -1, 7072, -1, 6847, -1], 'generators': [42], 'label': '256.6149.32.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.b1', 'old_label': '32.p1.b1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399376
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1'], 'contains': ['64.h1.a1', '64.j1.a1', '64.j1.c1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4287, -1, 9871, -1, 4336, -1, 9895, -1], 'generators': [34, 16], 'label': '256.6149.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.q1.a1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399377
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1'], 'contains': ['64.h1.a1', '64.j1.b1', '64.j1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4287, -1, 9386, -1, 4336, -1, 9408, -1], 'generators': [162, 16], 'label': '256.6149.32.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.q1.b1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399378
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1'], 'contains': ['64.h1.b1', '64.j1.a1', '64.j1.d1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4287, -1, 9143, -1, 4336, -1, 9165, -1], 'generators': [34, 144], 'label': '256.6149.32.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.q1.c1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399379
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1'], 'contains': ['64.h1.b1', '64.j1.b1', '64.j1.c1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4287, -1, 9628, -1, 4336, -1, 9651, -1], 'generators': [162, 144], 'label': '256.6149.32.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.q1.d1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399380
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.n1.a1', '32.n1.b1', '32.n1.c1', '32.n1.d1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.b1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7459, 2879, 7784, 5036, 7593, 2860, 7803, 4972], 'generators': [16, 128], 'label': '256.6149.64.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.b1.a1', '128.b1.b1', '128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.115', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.115', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399381
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'contains': ['128.a1.a1', '128.c1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6477, 3799, 7195, 4187, 6550, 3774, 7212, 4135], 'generators': [212, 128], 'label': '256.6149.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.3', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399382
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '32.o1.a1', '32.o1.b1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6222, 4718, 8343, 4741, 6291, 4688, 8363, 4681], 'generators': [196, 128], 'label': '256.6149.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.36', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399402
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.h1.a1', '64.h1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6477, -1, 8334, -1, 6550, -1, 8354, -1], 'generators': [212], 'label': '256.6149.128.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.c1.a1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399383
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2323', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.b1', '2.e1.b1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.e1.b1', '8.l1.b1', '8.m1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6459, 4707, 5101, 5291, 6418, 4706, 5113, 5224], 'generators': [40, 2, 192], 'label': '256.6149.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1', '2.e1.b1', '2.d1.b1'], 'normal_contains': ['8.b1.b1', '8.c1.a1', '8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399384
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '32.h1.a1', '32.i1.a1', '32.j1.a1', '32.k1.a1'], 'contains': ['128.a1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4337, 7006, 4052, 6413, 4386, 6962, 3980, 6381], 'generators': [4], 'label': '256.6149.64.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1.a1', 'normal_contained_in': ['32.b1.a1', '32.f1.a1', '32.d1.a1', '32.i1.a1', '32.h1.a1', '32.k1.a1', '32.j1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '64.70', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.70', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399385
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '32.p1.a1', '32.p1.b1'], 'contains': ['128.a1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6943, 4259, 6738, 4464, 7021, 4231, 6754, 4408], 'generators': [20], 'label': '256.6149.64.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.e1.a1', 'normal_contained_in': ['32.b1.a1', '32.g1.a1', '32.e1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '64.117', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.117', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399386
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.d1.a1', '32.g1.a1'], 'contains': ['128.a1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 3339, 7057, 3911, 6794, 3317, 7074, 3862], 'generators': [208], 'label': '256.6149.64.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.f1.a1', 'normal_contained_in': ['32.c1.a1', '32.g1.a1', '32.d1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.3', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399387
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '64.g1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.e1.a1', '32.f1.a1', '32.l1.a1', '32.l1.b1', '32.m1.a1', '32.m1.b1'], 'contains': ['128.a1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7217, 2378, 6132, 3264, 7349, 2362, 6118, 3223], 'generators': [192], 'label': '256.6149.64.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.g1.a1', 'normal_contained_in': ['32.c1.a1', '32.f1.a1', '32.e1.a1', '32.m1.b1', '32.m1.a1', '32.l1.a1', '32.l1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.671', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.36', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399388
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.q1.a1', '32.q1.b1'], 'contains': ['128.b1.a1', '128.c1.a1', '128.d1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5965, -1, 8635, -1, 6032, -1, 8656, -1], 'generators': [16, 196], 'label': '256.6149.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399389
    {'ambient': '256.6149', 'aut_centralizer_order': 1024, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.q1.c1', '32.q1.d1'], 'contains': ['128.b1.b1', '128.c1.a1', '128.d1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5965, -1, 8488, -1, 6032, -1, 8509, -1], 'generators': [144, 196], 'label': '256.6149.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.h1.b1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399390
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8159, -1, 8050, -1, 8300, -1, 8070, -1], 'generators': [8], 'label': '256.6149.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '64.i1.a1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399391
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.b1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8159, -1, 7921, -1, 8300, -1, 7941, -1], 'generators': [40], 'label': '256.6149.64.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.c1', 'old_label': '64.i1.b1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399392
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.c1'], 'contains': ['128.b1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8159, -1, 8193, -1, 8300, -1, 8213, -1], 'generators': [12], 'label': '256.6149.64.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.b1', 'old_label': '64.i1.c1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399393
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.d1'], 'contains': ['128.b1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8159, -1, 7596, -1, 8300, -1, 7614, -1], 'generators': [44], 'label': '256.6149.64.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.d1', 'old_label': '64.i1.d1', 'projective_image': '128.902', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399394
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6344767', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.b1.b1', '8.d1.a1', '8.g1.a1', '8.g1.b1', '8.h1.a1', '8.h1.b1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8764, 1523, 8255, 1370, 8863, 1543, 8273, 1352], 'generators': [8, 32, 4], 'label': '256.6149.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.b1.b1', '8.d1.a1', '8.h1.a1', '8.h1.b1', '8.g1.a1', '8.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399395
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.q1.a1', '32.q1.c1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 9157, -1, 5625, -1, 9180, -1], 'generators': [34], 'label': '256.6149.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.j1.a1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399396
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.q1.b1', '32.q1.d1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 8901, -1, 5625, -1, 8922, -1], 'generators': [162], 'label': '256.6149.64.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.j1.b1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399397
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.b1', '32.q1.a1', '32.q1.d1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 9029, -1, 5625, -1, 9051, -1], 'generators': [50], 'label': '256.6149.64.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.j1.c1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399398
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.b1', '32.q1.b1', '32.q1.c1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5562, -1, 8772, -1, 5625, -1, 8793, -1], 'generators': [178], 'label': '256.6149.64.j1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.j1.d1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399399
    {'ambient': '256.6149', 'aut_centralizer_order': 4096, 'aut_label': '128.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6711, 3566, 7126, 4494, 6784, 3543, 7144, 4437], 'generators': [128], 'label': '256.6149.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.c1.a1', '64.b1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.671', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.671', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399400
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '128.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.h1.a1', '64.i1.a1', '64.i1.b1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7174, 3124, 8050, 4777, 7302, 3104, 8070, 4717], 'generators': [16], 'label': '256.6149.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': '128.902', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.902', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399401
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '128.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.h1.b1', '64.i1.c1', '64.i1.d1'], 'contains': ['256.a1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7174, 3124, 7921, 5036, 7302, 3104, 7941, 4972], 'generators': [144], 'label': '256.6149.128.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.b1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.b1', 'projective_image': '128.902', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.902', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399403
    {'ambient': '256.6149', 'aut_centralizer_order': 2048, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.h1.a1', '64.h1.b1', '64.j1.a1', '64.j1.b1', '64.j1.c1', '64.j1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6094, -1, 8703, -1, 6162, -1, 8724, -1], 'generators': [196], 'label': '256.6149.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.d1.a1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399404
    {'ambient': '256.6149', '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.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.b1.b1', '128.c1.a1', '128.d1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6593, 3345, 8050, 4777, 6664, 3317, 8070, 4717], 'generators': [], 'label': '256.6149.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.b1.a1', '128.b1.b1', '128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.6149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399405
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.263', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.f1.b1', '8.p1.a1', '8.s1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1580, 9539, 1946, 8998, 1594, 9507, 1980, 8884], 'generators': [1, 16, 192], 'label': '256.6149.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399406
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.263', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.e1.b1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.i1.b1', '8.o1.a1', '8.t1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3750, 8440, 1007, 8336, 3793, 8415, 1009, 8231], 'generators': [33, 16, 192], 'label': '256.6149.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.e1.b1'], 'normal_contains': ['8.c1.a1', '8.i1.a1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399407
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2325', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.b1'], 'contains': ['8.c1.a1', '8.n1.a1', '8.q1.a1', '8.u1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2604, 7228, 3490, 7606, 2633, 7211, 3499, 7510], 'generators': [9, 16, 192], 'label': '256.6149.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.b1', '2.d1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399408
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2325', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.e1.a1'], 'contains': ['8.c1.a1', '8.n1.b1', '8.q1.b1', '8.u1.b1'], 'core': '4.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2604, 7228, 2767, 6809, 2633, 7211, 2773, 6722], 'generators': [41, 16, 192], 'label': '256.6149.4.g1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.b1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.d1.b1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399409
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6344767', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.e1.b1', '8.r1.a1', '8.r1.b1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8049, 2550, 6599, 3282, 8136, 2564, 6498, 3241], 'generators': [10, 32, 4], 'label': '256.6149.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.b1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399410
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dlg', 'aut_weyl_index': 4, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.h1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6824, 4134, 6147, 4241, 6847, 4136, 6103, 4188], 'generators': [8, 32, 2], 'label': '256.6149.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399411
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.260', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.a1', '8.l1.a1', '8.n1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 3941, -1, 2093, -1, 3917, -1], 'generators': [1, 8], 'label': '256.6149.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.i1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399412
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.260', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.b1', '8.l1.a1', '8.n1.a1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 4178, -1, 2093, -1, 4153, -1], 'generators': [193, 8], 'label': '256.6149.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.i1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399413
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.260', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1'], 'contains': ['8.f1.a1', '8.l1.b1', '8.n1.b1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 2250, -1, 2093, -1, 2255, -1], 'generators': [1, 40], 'label': '256.6149.4.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '4.i1.c1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399414
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.260', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1'], 'contains': ['8.f1.b1', '8.l1.b1', '8.n1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 2461, -1, 2093, -1, 2468, -1], 'generators': [193, 40], 'label': '256.6149.4.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '4.i1.d1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399415
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.263', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.k1.a1', '8.s1.a1', '8.t1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3206, -1, 1332, -1, 3243, -1, 1352, -1], 'generators': [1, 32], 'label': '256.6149.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.j1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399416
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.263', 'aut_weyl_index': 64, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.k1.b1', '8.s1.a1', '8.t1.a1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3206, -1, 1633, -1, 3243, -1, 1660, -1], 'generators': [1, 48], 'label': '256.6149.4.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.j1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399417
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2312', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.k1.a1', '8.u1.a1', '8.u1.b1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4181, -1, 3047, -1, 4228, -1, 3054, -1], 'generators': [9, 32], 'label': '256.6149.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.k1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399418
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2312', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.k1.b1', '8.u1.a1', '8.u1.b1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4181, -1, 3211, -1, 4228, -1, 3218, -1], 'generators': [9, 48], 'label': '256.6149.4.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.k1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399419
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.j1.b1', '16.n1.a1', '16.s1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5756, 5036, 7520, 5011, 5821, 5003, 7539, 4948], 'generators': [34, 16, 4], 'label': '256.6149.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'normal_contains': ['16.a1.a1', '16.j1.a1', '16.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399420
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.c1', '16.o1.a1', '16.p1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7952, 2712, 8134, 2246, 8041, 2694, 8154, 2218], 'generators': [8, 192, 4], 'label': '256.6149.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.d1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399421
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55647', 'aut_weyl_index': 16, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '4.j1.a1', '4.j1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3416, 8888, 1792, 8998, 3455, 8860, 1821, 8884], 'generators': [1, 32, 16], 'label': '256.6149.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.f1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399422
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'contains': ['16.a1.a1', '16.d1.b1', '16.d1.d1', '16.o1.b1', '16.p1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7952, 2712, 7819, 1611, 8041, 2694, 7837, 1590], 'generators': [40, 192, 4], 'label': '256.6149.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.b1', '16.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399423
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.e1.a1', '4.f1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.g1.a1', '16.h1.a1', '16.k1.a1', '16.l1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3394, 7604, 3455, 7534, 3432, 7555, 3463, 7439], 'generators': [2, 16, 192], 'label': '256.6149.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.f1.a1', '4.e1.a1', '4.g1.b1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.l1.a1', '16.k1.a1', '16.h1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399424
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.f1.a1', '16.i1.a1', '16.i1.b1', '16.m1.a1', '16.m1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8764, 1714, 6119, 2847, 8863, 1703, 6134, 2811], 'generators': [32, 16, 4], 'label': '256.6149.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.a1', '4.h1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.e1.a1', '16.m1.b1', '16.m1.a1', '16.i1.a1', '16.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '32.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399425
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.a1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.q1.a1', '16.r1.a1', '16.t1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7330, 3901, 6458, 3529, 7413, 3875, 6473, 3485], 'generators': [10, 192, 4], 'label': '256.6149.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.b1', '4.c1.a1', '4.h1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399426
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.b1', '4.h1.a1'], 'contains': ['16.a1.a1', '16.q1.b1', '16.r1.b1', '16.t1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7330, 3901, 7181, 4328, 7413, 3875, 7199, 4273], 'generators': [42, 192, 4], 'label': '256.6149.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.a1.a1', '4.c1.b1', '4.h1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399427
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.i1.c1'], 'contains': ['16.b1.a1', '16.u1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [736, 9622, 1873, 9281, 744, 9555, 1878, 9164], 'generators': [1, 16], 'label': '256.6149.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399428
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.b1', '4.i1.d1'], 'contains': ['16.b1.a1', '16.u1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [736, 9622, 2164, 9867, 744, 9555, 2169, 9743], 'generators': [193, 16], 'label': '256.6149.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399429
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.d1.a1', '16.d1.b1', '16.e1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9443, 968, 8703, 1125, 9548, 961, 8724, 1111], 'generators': [8, 32], 'label': '256.6149.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.a1', '16.d1.b1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399430
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.d1.c1', '16.d1.d1', '16.e1.a1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9443, 968, 8538, 464, 9548, 961, 8559, 458], 'generators': [12, 32], 'label': '256.6149.8.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.c1', '16.d1.d1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.b1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399431
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.d1.a1', '16.d1.d1', '16.f1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9155, 419, 8374, 133, 9258, 415, 8395, 131], 'generators': [8, 36], 'label': '256.6149.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.a1', '16.d1.d1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399432
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dms', 'aut_weyl_index': 4, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.g1.a1', '4.g1.b1', '4.k1.a1', '4.k1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4050, 5573, 3203, 5737, 4096, 5567, 3211, 5665], 'generators': [9, 32, 16], 'label': '256.6149.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.g1.b1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399433
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.d1.b1', '16.d1.c1', '16.f1.a1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9155, 419, 8867, 794, 9258, 415, 8888, 784], 'generators': [12, 36], 'label': '256.6149.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.b1', '16.d1.c1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399434
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.i1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.g1.a1', '16.w1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3894, 8626, 129, 8110, 3938, 8558, 130, 8007], 'generators': [33, 208], 'label': '256.6149.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399435
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.i1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.g1.a1', '16.w1.b1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3894, 8626, 711, 8696, 3938, 8558, 712, 8586], 'generators': [225, 208], 'label': '256.6149.8.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399436
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.j1.a1', '16.k1.a1', '16.m1.b1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5297, 6726, 4737, 6028, 5356, 6682, 4748, 5952], 'generators': [48, 18], 'label': '256.6149.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.a1', '16.k1.a1', '16.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399437
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.j1.b1', '16.k1.a1', '16.m1.a1'], 'core': '8.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5297, 6726, 4494, 7006, 5356, 6682, 4505, 6917], 'generators': [32, 18], 'label': '256.6149.8.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.b1', '16.k1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399438
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.k1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.j1.a1', '16.l1.a1', '16.m1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4872, 5914, 3717, 6517, 4927, 5875, 3726, 6435], 'generators': [32, 2], 'label': '256.6149.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.a1', '16.l1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '32.28', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399439
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '8.k1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.b1', '4.k1.b1'], 'contains': ['16.j1.b1', '16.l1.a1', '16.m1.b1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4872, 5914, 3960, 5539, 4927, 5875, 3969, 5469], 'generators': [48, 2], 'label': '256.6149.8.k1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.b1', '16.l1.a1', '16.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.b1', 'projective_image': '32.28', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399440
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.b1.a1', '16.p1.a1', '16.q1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6216, -1, 5222, -1, 6285, -1, 5235, -1], 'generators': [8, 2], 'label': '256.6149.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.l1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399441
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.i1.c1', '4.i1.d1'], 'contains': ['16.b1.a1', '16.p1.b1', '16.q1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6216, -1, 4980, -1, 6285, -1, 4992, -1], 'generators': [40, 2], 'label': '256.6149.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '8.l1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399442
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.c1.a1', '16.p1.a1', '16.q1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6705, -1, 5819, -1, 6781, -1, 5833, -1], 'generators': [8, 194], 'label': '256.6149.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399443
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '512.10493147', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1', '4.i1.a1', '4.i1.b1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2604, 7586, 3851, 8213, 2633, 7567, 3826, 8110], 'generators': [1, 8, 192], 'label': '256.6149.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399444
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1'], 'contains': ['16.c1.a1', '16.p1.b1', '16.q1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6705, -1, 5502, -1, 6781, -1, 5515, -1], 'generators': [40, 194], 'label': '256.6149.8.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '8.m1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399445
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '8.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.b1.a1', '16.v1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 4227, -1, 2093, -1, 4237, -1], 'generators': [9, 16], 'label': '256.6149.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.n1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399446
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '8.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '4.i1.c1', '4.i1.d1'], 'contains': ['16.b1.a1', '16.v1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2069, -1, 2454, -1, 2093, -1, 2460, -1], 'generators': [41, 16], 'label': '256.6149.8.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '8.n1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399447
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.c1.a1', '16.w1.a1', '16.w1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4403, -1, 420, -1, 4453, -1, 421, -1], 'generators': [33, 16], 'label': '256.6149.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399448
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.h1.a1', '16.u1.a1', '16.u1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [227, -1, 1583, -1, 229, -1, 1586, -1], 'generators': [1, 208], 'label': '256.6149.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399449
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.h1.a1', '16.v1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1149, -1, 3225, -1, 1161, -1, 3233, -1], 'generators': [9, 208], 'label': '256.6149.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '8.q1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399450
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1'], 'contains': ['16.h1.a1', '16.v1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1149, -1, 2690, -1, 1161, -1, 2696, -1], 'generators': [41, 208], 'label': '256.6149.8.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.q1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399451
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.i1.a1', '16.r1.a1', '16.r1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8374, -1, 6738, -1, 8468, -1, 6754, -1], 'generators': [10, 32], 'label': '256.6149.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399452
    {'ambient': '256.6149', 'aut_centralizer_order': 16, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.i1.b1', '16.r1.a1', '16.r1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8374, -1, 6901, -1, 8468, -1, 6918, -1], 'generators': [10, 36], 'label': '256.6149.8.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.b1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399453
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.l1.a1', '16.u1.a1', '16.u1.b1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1560, -1, 1292, -1, 1578, -1, 1295, -1], 'generators': [1, 192], 'label': '256.6149.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399454
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '512.10493147', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.e1.a1', '4.g1.b1', '4.i1.c1', '4.i1.d1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2604, 7586, 2497, 7502, 2633, 7567, 2503, 7407], 'generators': [1, 40, 192], 'label': '256.6149.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.e1.a1', '4.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399455
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.l1.a1', '16.w1.a1', '16.w1.b1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2894, -1, 1002, -1, 2927, -1, 1004, -1], 'generators': [33, 192], 'label': '256.6149.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399456
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.l1.a1', '16.v1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2482, -1, 3047, -1, 2510, -1, 3054, -1], 'generators': [9, 192], 'label': '256.6149.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.u1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399457
    {'ambient': '256.6149', 'aut_centralizer_order': 32, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.l1.a1', '16.v1.b1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2482, -1, 2868, -1, 2510, -1, 2875, -1], 'generators': [41, 192], 'label': '256.6149.8.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.u1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399458
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6447, 4217, 7057, 4350, 6519, 4190, 7074, 4295], 'generators': [16, 192, 4], 'label': '256.6149.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1', '8.e1.b1', '8.e1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.f1.a1', '32.g1.a1', '32.d1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399459
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.f1.a1', '8.f1.b1', '8.l1.a1', '8.l1.b1', '8.n1.a1', '8.n1.b1'], 'contains': ['32.b1.a1', '32.h1.a1', '32.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2582, 9647, 3578, 8400, 2611, 9585, 3658, 8294], 'generators': [2, 16], 'label': '256.6149.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.c1.a1', '8.f1.a1', '8.f1.b1'], 'normal_contains': ['32.b1.a1', '32.i1.a1', '32.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '16.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399460
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.m1.a1', '8.m1.b1', '8.o1.a1'], 'contains': ['32.b1.a1', '32.j1.a1', '32.k1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4556, 6397, 4220, 7423, 4608, 6356, 4230, 7329], 'generators': [194, 16], 'label': '256.6149.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.b1.a1', '32.k1.a1', '32.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399461
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.c1.a1', '32.n1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9773, 1033, 8108, 1125, 9883, 1027, 8127, 1111], 'generators': [8, 192], 'label': '256.6149.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.h1.a1', '8.g1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399462
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.g1.a1', '8.h1.b1'], 'contains': ['32.c1.a1', '32.n1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9773, 1033, 8272, 1944, 9883, 1027, 8291, 1920], 'generators': [40, 192], 'label': '256.6149.16.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': ['8.b1.b1', '8.h1.b1', '8.g1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399463
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.g1.b1', '8.h1.b1'], 'contains': ['32.c1.a1', '32.n1.c1'], 'core': '16.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9773, 1033, 8639, 794, 9883, 1027, 8659, 784], 'generators': [12, 192], 'label': '256.6149.16.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.c1', 'normal_contained_in': ['8.b1.a1', '8.h1.b1', '8.g1.b1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.c1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399464
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.g1.b1', '8.h1.a1'], 'contains': ['32.c1.a1', '32.n1.d1'], 'core': '16.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9773, 1033, 7943, 464, 9883, 1027, 7962, 458], 'generators': [44, 192], 'label': '256.6149.16.d1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.d1', 'normal_contained_in': ['8.b1.b1', '8.h1.a1', '8.g1.b1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.d1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399465
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '512.10493147', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4553, 6534, 2881, 6315, 4604, 6522, 2888, 6236], 'generators': [33, 8], 'label': '256.6149.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.f1.a1', '4.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399466
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.g1.a1', '8.g1.b1'], 'contains': ['32.c1.a1', '32.l1.a1', '32.l1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9417, 1714, 7319, 2354, 9523, 1703, 7337, 2325], 'generators': [32, 16], 'label': '256.6149.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.d1.a1', '8.g1.a1', '8.g1.b1'], 'normal_contains': ['32.c1.a1', '32.l1.a1', '32.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '64.115', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399467
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.c1.a1', '32.m1.a1', '32.m1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8992, 353, 7561, 1534, 9093, 350, 7580, 1516], 'generators': [36, 16], 'label': '256.6149.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.d1.a1', '8.h1.a1', '8.h1.b1'], 'normal_contains': ['32.c1.a1', '32.m1.b1', '32.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '64.115', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399468
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.i1.a1', '8.i1.b1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.k1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3432, 8835, 1707, 7911, 3470, 8778, 1712, 7812], 'generators': [194, 208], 'label': '256.6149.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1', '8.i1.a1', '8.i1.b1'], 'normal_contains': ['32.d1.a1', '32.h1.a1', '32.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399469
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.h1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.p1.a1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.d1.a1', '32.i1.a1', '32.j1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2157, 8023, 2890, 6934, 2181, 7970, 2897, 6847], 'generators': [2, 208], 'label': '256.6149.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.d1.a1', '32.i1.a1', '32.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '32.28', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399470
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.i1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.r1.a1'], 'contains': ['32.e1.a1', '32.l1.a1', '32.m1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8567, 2526, 5725, 3332, 8664, 2510, 5739, 3290], 'generators': [32, 20], 'label': '256.6149.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.d1.a1'], 'normal_contains': ['32.e1.a1', '32.m1.b1', '32.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '64.117', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399471
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.i1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.r1.b1'], 'contains': ['32.e1.a1', '32.l1.b1', '32.m1.a1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8567, 2526, 5967, 2843, 8664, 2510, 5982, 2807], 'generators': [36, 20], 'label': '256.6149.16.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': ['8.d1.a1'], 'normal_contains': ['32.e1.a1', '32.m1.a1', '32.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.b1', 'projective_image': '64.117', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399472
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.j1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.j1.a1', '8.k1.a1'], 'contains': ['32.f1.a1', '32.o1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4897, 4934, 5046, 5270, 4952, 4902, 5058, 5203], 'generators': [34, 4], 'label': '256.6149.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.a1.a1', '8.k1.a1', '8.j1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399493
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.p1.a1', '8.s1.a1'], 'contains': ['32.i1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1120, -1, 2129, -1, 1161, -1, 2135, -1], 'generators': [193], 'label': '256.6149.16.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.u1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399473
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.j1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.j1.b1', '8.k1.b1'], 'contains': ['32.f1.a1', '32.o1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4897, 4934, 4899, 5564, 4952, 4902, 4911, 5494], 'generators': [50, 4], 'label': '256.6149.16.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': ['8.a1.a1', '8.k1.b1', '8.j1.b1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.b1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399474
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.k1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.f1.a1', '32.h1.a1', '32.j1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4131, 7209, 3977, 6445, 4178, 7163, 3987, 6364], 'generators': [18, 192], 'label': '256.6149.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.c1.a1', '8.j1.a1', '8.j1.b1'], 'normal_contains': ['32.f1.a1', '32.h1.a1', '32.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '32.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399475
    {'ambient': '256.6149', 'aut_centralizer_order': 512, 'aut_label': '16.l1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.k1.a1', '8.k1.b1', '8.s1.a1', '8.t1.a1', '8.u1.a1', '8.u1.b1'], 'contains': ['32.f1.a1', '32.i1.a1', '32.k1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3007, 5585, 3132, 5956, 3041, 5549, 3140, 5881], 'generators': [2, 192], 'label': '256.6149.16.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': ['8.c1.a1', '8.k1.a1', '8.k1.b1'], 'normal_contains': ['32.f1.a1', '32.i1.a1', '32.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.l1.a1', 'projective_image': '32.28', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399476
    {'ambient': '256.6149', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '512.10493147', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.f1.a1', '4.g1.a1'], 'core': '2.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4553, 6534, 3490, 6870, 4604, 6522, 3499, 6783], 'generators': [33, 40], 'label': '256.6149.2.e1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399477
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.m1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.j1.b1', '8.k1.a1'], 'contains': ['32.f1.a1', '32.l1.a1', '32.m1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7217, 3339, 4463, 4878, 7299, 3317, 4473, 4816], 'generators': [32, 4], 'label': '256.6149.16.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': ['8.d1.a1', '8.k1.a1', '8.j1.b1'], 'normal_contains': ['32.f1.a1', '32.m1.a1', '32.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399478
    {'ambient': '256.6149', 'aut_centralizer_order': 256, 'aut_label': '16.m1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.j1.a1', '8.k1.b1'], 'contains': ['32.f1.a1', '32.l1.b1', '32.m1.b1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7217, 3339, 4705, 3821, 7299, 3317, 4716, 3773], 'generators': [48, 4], 'label': '256.6149.16.m1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.b1', 'normal_contained_in': ['8.d1.a1', '8.k1.b1', '8.j1.a1'], 'normal_contains': ['32.f1.a1', '32.m1.b1', '32.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.m1.b1', 'projective_image': '64.70', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399479
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.a1.a1', '32.o1.a1', '32.o1.b1', '32.q1.a1', '32.q1.b1', '32.q1.c1', '32.q1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5271, -1, 9211, -1, 5331, -1, 9233, -1], 'generators': [34, 16, 128], 'label': '256.6149.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399480
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.a1.a1', '32.n1.a1', '32.n1.c1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8177, -1, 8822, -1, 8269, -1, 8844, -1], 'generators': [8, 196], 'label': '256.6149.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.o1.a1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399481
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1'], 'contains': ['32.a1.a1', '32.n1.b1', '32.n1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8177, -1, 8455, -1, 8269, -1, 8475, -1], 'generators': [40, 196], 'label': '256.6149.16.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '16.o1.b1', 'projective_image': '64.115', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 50399482
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '32.n1.a1', '32.n1.c1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7558, -1, 6486, -1, 7643, -1, 6502, -1], 'generators': [8, 4], 'label': '256.6149.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.p1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399483
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.l1.b1', '8.m1.b1'], 'contains': ['32.b1.a1', '32.n1.b1', '32.n1.d1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7558, -1, 6340, -1, 7643, -1, 6355, -1], 'generators': [40, 4], 'label': '256.6149.16.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '16.p1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399484
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '32.p1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5987, -1, 5240, -1, 6054, -1, 5252, -1], 'generators': [10, 4], 'label': '256.6149.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.q1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399485
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.l1.b1', '8.m1.b1'], 'contains': ['32.b1.a1', '32.p1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5987, -1, 5482, -1, 6054, -1, 5496, -1], 'generators': [42, 4], 'label': '256.6149.16.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '16.q1.b1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 50399486
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.r1.a1', '8.r1.b1'], 'contains': ['32.e1.a1', '32.p1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7843, -1, 6649, -1, 7931, -1, 6665, -1], 'generators': [10, 192], 'label': '256.6149.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.r1.a1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399487
    {'ambient': '256.6149', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.e1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7190, 3584, 7411, 3903, 7277, 3590, 7369, 3854], 'generators': [8, 34], 'label': '256.6149.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 50399488
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.r1.a1', '8.r1.b1'], 'contains': ['32.e1.a1', '32.p1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7843, -1, 6827, -1, 7931, -1, 6843, -1], 'generators': [42, 192], 'label': '256.6149.16.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.r1.b1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399489
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.g1.a1', '32.o1.a1', '32.o1.b1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5647, -1, 8997, -1, 5710, -1, 9019, -1], 'generators': [34, 20], 'label': '256.6149.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.s1.a1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399490
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.g1.a1', '32.p1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6849, -1, 6178, -1, 6926, -1, 6193, -1], 'generators': [10, 196], 'label': '256.6149.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.t1.a1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399491
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1'], 'contains': ['32.g1.a1', '32.p1.b1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6849, -1, 7772, -1, 6926, -1, 7791, -1], 'generators': [42, 196], 'label': '256.6149.16.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.b1', 'old_label': '16.t1.b1', 'projective_image': '64.117', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 50399492
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.p1.a1', '8.s1.a1'], 'contains': ['32.i1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1120, -1, 1908, -1, 1161, -1, 1912, -1], 'generators': [1], 'label': '256.6149.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.u1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399494
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '8.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.q1.a1', '8.u1.a1'], 'contains': ['32.i1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1807, -1, 3332, -1, 1828, -1, 3340, -1], 'generators': [9], 'label': '256.6149.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.v1.a1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399495
    {'ambient': '256.6149', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '8.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '8.q1.b1', '8.u1.b1'], 'contains': ['32.i1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1807, -1, 2690, -1, 1828, -1, 2696, -1], 'generators': [41], 'label': '256.6149.16.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '16.v1.b1', 'projective_image': '32.28', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 50399496
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.o1.a1', '8.t1.a1'], 'contains': ['32.k1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3781, -1, 527, -1, 3824, -1, 634, -1], 'generators': [33], 'label': '256.6149.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.w1.a1', 'projective_image': '64.70', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 50399497
    {'ambient': '256.6149', 'aut_centralizer_order': 128, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.o1.a1', '8.t1.a1'], 'contains': ['32.k1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3781, -1, 896, -1, 3824, -1, 857, -1], 'generators': [49], 'label': '256.6149.16.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.w1.b1', 'projective_image': '64.70', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}