Abstract group data - 176.33

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [10, 2, 6, 2, 22], 'aut_gens': [[1, 2, 4], [1, 90, 52], [132, 2, 49], [132, 2, 173], [89, 2, 92], [89, 130, 4]], 'aut_group': '5280.ba', 'aut_hash': 96918778551754254, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5280, 'aut_permdeg': 17, 'aut_perms': [4485056047920, 289, 1322060025311, 126, 155900694741241], 'aut_phi_ratio': 66.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [4, 2, 3, 1], [4, 22, 3, 1], [11, 2, 5, 1], [22, 2, 5, 1], [44, 4, 15, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_4\\times F_{11}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [4, 2, 3], [4, 22, 3], [11, 2, 5], [22, 2, 5], [44, 4, 15]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '88.11', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 33, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['22.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [4, 2, 1, 3], [4, 22, 1, 3], [11, 2, 5, 1], [22, 2, 5, 1], [44, 4, 5, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 44, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 11], 'faithful_reps': [[4, -1, 5]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '88.11', 'hash': 33, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 2, 22], 'inner_gens': [[1, 2, 92], [1, 2, 84], [89, 98, 4]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 88, 'inner_split': True, 'inner_tex': 'C_2\\times D_{22}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 20, 'irrQ_dim': 40, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 22], [4, 5]], 'label': '176.33', 'linC_count': 45, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 8, 'linQ_dim': 14, 'linQ_dim_count': 8, 'linR_count': 40, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'Q8*D11', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 35, 'number_divisions': 15, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 20, 'number_subgroup_classes': 38, 'number_subgroups': 168, 'old_label': None, 'order': 176, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 23], [4, 72], [11, 10], [22, 10], [44, 60]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 30], 'outer_gen_pows': [1, 0], 'outer_gens': [[1, 2, 85], [44, 90, 157]], 'outer_group': '60.11', 'outer_hash': 11, 'outer_nilpotent': False, 'outer_order': 60, 'outer_permdeg': 10, 'outer_perms': [1, 816507], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [10, 4], [20, 1]], 'representations': {'PC': {'code': 441041520141218794900009, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -11, 440, 1382, 637, 42, 1688, 58, 2009]}, 'GLZN': {'d': 2, 'p': 33, 'gens': [826574, 36037, 384086, 48302, 443772]}, 'Perm': {'d': 19, 'gens': [357001369769809, 12460, 18523, 5329, 7116376444894080]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8\\times D_{11}', 'transitive_degree': 88, '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: 109045041
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 33, 'group_order': 176, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109045052
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 33, 'group_order': 176, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 88, 'size': 1}
  • id: 109045063
    {'aut_label': '2B', 'centralizer': '11.a1.a1', 'counter': 3, 'group_counter': 33, 'group_order': 176, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2, 'size': 11}
  • id: 109045070
    {'aut_label': '2B', 'centralizer': '11.a1.a1', 'counter': 4, 'group_counter': 33, 'group_order': 176, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 10, 'size': 11}
  • id: 109045071
    {'aut_label': '4A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 33, 'group_order': 176, 'label': '4A', 'order': 4, 'powers': [2, 5, 5], 'representative': 44, 'size': 2}
  • id: 109045072
    {'aut_label': '4A', 'centralizer': '2.a1.b1', 'counter': 6, 'group_counter': 33, 'group_order': 176, 'label': '4B', 'order': 4, 'powers': [2, 6, 6], 'representative': 89, 'size': 2}
  • id: 109045073
    {'aut_label': '4A', 'centralizer': '2.a1.c1', 'counter': 7, 'group_counter': 33, 'group_order': 176, 'label': '4C', 'order': 4, 'powers': [2, 7, 7], 'representative': 45, 'size': 2}
  • id: 109045074
    {'aut_label': '4D', 'centralizer': '22.b1.a1', 'counter': 8, 'group_counter': 33, 'group_order': 176, 'label': '4D', 'order': 4, 'powers': [2, 8, 8], 'representative': 158, 'size': 22}
  • id: 109045075
    {'aut_label': '4D', 'centralizer': '22.b1.b1', 'counter': 9, 'group_counter': 33, 'group_order': 176, 'label': '4E', 'order': 4, 'powers': [2, 9, 9], 'representative': 51, 'size': 22}
  • id: 109045042
    {'aut_label': '4D', 'centralizer': '22.b1.c1', 'counter': 10, 'group_counter': 33, 'group_order': 176, 'label': '4F', 'order': 4, 'powers': [2, 10, 10], 'representative': 127, 'size': 22}
  • id: 109045043
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 11, 'group_counter': 33, 'group_order': 176, 'label': '11A1', 'order': 11, 'powers': [12, 15, 1], 'representative': 16, 'size': 2}
  • id: 109045044
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 33, 'group_order': 176, 'label': '11A2', 'order': 11, 'powers': [14, 11, 1], 'representative': 32, 'size': 2}
  • id: 109045045
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 13, 'group_counter': 33, 'group_order': 176, 'label': '11A3', 'order': 11, 'powers': [15, 14, 1], 'representative': 48, 'size': 2}
  • id: 109045046
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 14, 'group_counter': 33, 'group_order': 176, 'label': '11A4', 'order': 11, 'powers': [13, 12, 1], 'representative': 64, 'size': 2}
  • id: 109045047
    {'aut_label': '11A1', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 33, 'group_order': 176, 'label': '11A5', 'order': 11, 'powers': [11, 13, 1], 'representative': 80, 'size': 2}
  • id: 109045048
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 33, 'group_order': 176, 'label': '22A1', 'order': 22, 'powers': [11, 18, 2], 'representative': 8, 'size': 2}
  • id: 109045049
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 17, 'group_counter': 33, 'group_order': 176, 'label': '22A3', 'order': 22, 'powers': [13, 19, 2], 'representative': 24, 'size': 2}
  • id: 109045050
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 18, 'group_counter': 33, 'group_order': 176, 'label': '22A5', 'order': 22, 'powers': [15, 17, 2], 'representative': 40, 'size': 2}
  • id: 109045051
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 33, 'group_order': 176, 'label': '22A7', 'order': 22, 'powers': [14, 20, 2], 'representative': 56, 'size': 2}
  • id: 109045053
    {'aut_label': '22A1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 33, 'group_order': 176, 'label': '22A9', 'order': 22, 'powers': [12, 16, 2], 'representative': 72, 'size': 2}
  • id: 109045054
    {'aut_label': '44A1', 'centralizer': '4.b1.a1', 'counter': 21, 'group_counter': 33, 'group_order': 176, 'label': '44A1', 'order': 44, 'powers': [16, 23, 5], 'representative': 4, 'size': 4}
  • id: 109045055
    {'aut_label': '44A1', 'centralizer': '4.b1.a1', 'counter': 22, 'group_counter': 33, 'group_order': 176, 'label': '44A3', 'order': 44, 'powers': [17, 24, 5], 'representative': 12, 'size': 4}
  • id: 109045056
    {'aut_label': '44A1', 'centralizer': '4.b1.a1', 'counter': 23, 'group_counter': 33, 'group_order': 176, 'label': '44A5', 'order': 44, 'powers': [18, 22, 5], 'representative': 20, 'size': 4}
  • id: 109045057
    {'aut_label': '44A1', 'centralizer': '4.b1.a1', 'counter': 24, 'group_counter': 33, 'group_order': 176, 'label': '44A7', 'order': 44, 'powers': [19, 25, 5], 'representative': 116, 'size': 4}
  • id: 109045058
    {'aut_label': '44A1', 'centralizer': '4.b1.a1', 'counter': 25, 'group_counter': 33, 'group_order': 176, 'label': '44A9', 'order': 44, 'powers': [20, 21, 5], 'representative': 36, 'size': 4}
  • id: 109045059
    {'aut_label': '44A1', 'centralizer': '4.b1.b1', 'counter': 26, 'group_counter': 33, 'group_order': 176, 'label': '44B1', 'order': 44, 'powers': [19, 28, 6], 'representative': 17, 'size': 4}
  • id: 109045060
    {'aut_label': '44A1', 'centralizer': '4.b1.b1', 'counter': 27, 'group_counter': 33, 'group_order': 176, 'label': '44B3', 'order': 44, 'powers': [16, 29, 6], 'representative': 49, 'size': 4}
  • id: 109045061
    {'aut_label': '44A1', 'centralizer': '4.b1.b1', 'counter': 28, 'group_counter': 33, 'group_order': 176, 'label': '44B5', 'order': 44, 'powers': [20, 27, 6], 'representative': 9, 'size': 4}
  • id: 109045062
    {'aut_label': '44A1', 'centralizer': '4.b1.b1', 'counter': 29, 'group_counter': 33, 'group_order': 176, 'label': '44B7', 'order': 44, 'powers': [18, 30, 6], 'representative': 65, 'size': 4}
  • id: 109045064
    {'aut_label': '44A1', 'centralizer': '4.b1.b1', 'counter': 30, 'group_counter': 33, 'group_order': 176, 'label': '44B9', 'order': 44, 'powers': [17, 26, 6], 'representative': 33, 'size': 4}
  • id: 109045065
    {'aut_label': '44A1', 'centralizer': '4.b1.c1', 'counter': 31, 'group_counter': 33, 'group_order': 176, 'label': '44C1', 'order': 44, 'powers': [16, 33, 7], 'representative': 5, 'size': 4}
  • id: 109045066
    {'aut_label': '44A1', 'centralizer': '4.b1.c1', 'counter': 32, 'group_counter': 33, 'group_order': 176, 'label': '44C3', 'order': 44, 'powers': [17, 34, 7], 'representative': 13, 'size': 4}
  • id: 109045067
    {'aut_label': '44A1', 'centralizer': '4.b1.c1', 'counter': 33, 'group_counter': 33, 'group_order': 176, 'label': '44C5', 'order': 44, 'powers': [18, 32, 7], 'representative': 21, 'size': 4}
  • id: 109045068
    {'aut_label': '44A1', 'centralizer': '4.b1.c1', 'counter': 34, 'group_counter': 33, 'group_order': 176, 'label': '44C7', 'order': 44, 'powers': [19, 35, 7], 'representative': 117, 'size': 4}
  • id: 109045069
    {'aut_label': '44A1', 'centralizer': '4.b1.c1', 'counter': 35, 'group_counter': 33, 'group_order': 176, 'label': '44C9', 'order': 44, 'powers': [20, 31, 7], 'representative': 37, 'size': 4}
• 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: 4121124
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1a', '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], 'schur_index': 1}
  • id: 4121131
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1b', '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], 'schur_index': 1}
  • id: 4121132
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1c', '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], 'schur_index': 1}
  • id: 4121133
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1d', '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], 'schur_index': 1}
  • id: 4121134
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1e', '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], 'schur_index': 1}
  • id: 4121135
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1f', '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], 'schur_index': 1}
  • id: 4121136
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1g', '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], 'schur_index': 1}
  • id: 4121137
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.1h', '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], 'schur_index': 1}
  • id: 4121138
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2a', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 2}
  • id: 4121125
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2b', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 2}
  • id: 4121126
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2c', 'multiplicity': 5, 'nt': [11, 2], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 10, 10, 10, 0, 0, 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], 'schur_index': 1}
  • id: 4121127
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2d', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -10, -10, 10, 0, 0, 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], 'schur_index': 1}
  • id: 4121128
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2e', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, -10, 10, -10, 0, 0, 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], 'schur_index': 1}
  • id: 4121129
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.2f', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 10, -10, -10, 0, 0, 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], 'schur_index': 1}
  • id: 4121130
    {'cdim': 4, 'counter': 15, 'faithful': True, 'group': '176.33', 'group_order': 176, 'image': None, 'label': '176.33.4a', 'multiplicity': 5, 'nt': [88, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 2}
• 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: 5952738
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 176, 'label': '176.33.1a', '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]]]}
  • id: 5952749
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.c1', 'kernel_order': 88, 'label': '176.33.1b', '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]]]}
  • id: 5952760
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 88, 'label': '176.33.1c', '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]]]}
  • id: 5952767
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 88, 'label': '176.33.1d', '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]]]}
  • id: 5952768
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 88, 'label': '176.33.1e', '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]]]}
  • id: 5952769
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.c1', 'kernel_order': 88, 'label': '176.33.1f', '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]]]}
  • id: 5952770
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 88, 'label': '176.33.1g', '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]]]}
  • id: 5952771
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 176, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 88, 'label': '176.33.1h', '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]]]}
  • id: 5952772
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 44, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.b1.b1', 'kernel_order': 22, 'label': '176.33.2a', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-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]]]}
  • id: 5952739
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 44, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.b1.a1', 'kernel_order': 22, 'label': '176.33.2b', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-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]]]}
  • id: 5952740
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 11, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 8, 'label': '176.33.2c1', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]]]}
  • id: 5952741
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 12, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 8, 'label': '176.33.2c2', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]]]}
  • id: 5952742
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 13, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 8, 'label': '176.33.2c3', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 5952743
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 14, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 8, 'label': '176.33.2c4', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 5952744
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 15, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '22.1', 'image_order': 22, 'indicator': 1, 'kernel': '22.a1.a1', 'kernel_order': 8, 'label': '176.33.2c5', 'nt': [11, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]]]}
  • id: 5952745
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.c1', 'kernel_order': 4, 'label': '176.33.2d1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]]]}
  • id: 5952746
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.c1', 'kernel_order': 4, 'label': '176.33.2d2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]]]}
  • id: 5952747
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.c1', 'kernel_order': 4, 'label': '176.33.2d3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 5952748
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.c1', 'kernel_order': 4, 'label': '176.33.2d4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 5952750
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.c1', 'kernel_order': 4, 'label': '176.33.2d5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 5952751
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.b1', 'kernel_order': 4, 'label': '176.33.2e1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]]]}
  • id: 5952752
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.b1', 'kernel_order': 4, 'label': '176.33.2e2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]]]}
  • id: 5952753
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 23, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.b1', 'kernel_order': 4, 'label': '176.33.2e3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 5952754
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.b1', 'kernel_order': 4, 'label': '176.33.2e4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 5952755
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 25, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.b1', 'kernel_order': 4, 'label': '176.33.2e5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]]]}
  • id: 5952756
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 26, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 4, 'label': '176.33.2f1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]]]}
  • id: 5952757
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 27, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 4, 'label': '176.33.2f2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]]]}
  • id: 5952758
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 28, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 4, 'label': '176.33.2f3', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]]]}
  • id: 5952759
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 4, 'label': '176.33.2f4', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 5952761
    {'center': '22.a1.a1', 'center_index': 22, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.a1.a1', 'kernel_order': 4, 'label': '176.33.2f5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 5952762
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 11, 'dim': 4, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '176.33', 'image_order': 176, 'indicator': -1, 'kernel': '176.a1.a1', 'kernel_order': 1, 'label': '176.33.4a1', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 4], [-2, -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]]]}
  • id: 5952763
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 11, 'dim': 4, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '176.33', 'image_order': 176, 'indicator': -1, 'kernel': '176.a1.a1', 'kernel_order': 1, 'label': '176.33.4a2', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 5], [-2, -5]], [[-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]]]}
  • id: 5952764
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 11, 'dim': 4, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '176.33', 'image_order': 176, 'indicator': -1, 'kernel': '176.a1.a1', 'kernel_order': 1, 'label': '176.33.4a3', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 4], [-2, -4]], [[-2, 1], [-2, -1]], [[-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]]]}
  • id: 5952765
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 11, 'dim': 4, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '176.33', 'image_order': 176, 'indicator': -1, 'kernel': '176.a1.a1', 'kernel_order': 1, 'label': '176.33.4a4', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5952766
    {'center': '88.a1.a1', 'center_index': 88, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 11, 'dim': 4, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '176.33', 'group_counter': 33, 'group_order': 176, 'image': None, 'image_isoclass': '176.33', 'image_order': 176, 'indicator': -1, 'kernel': '176.a1.a1', 'kernel_order': 1, 'label': '176.33.4a5', 'nt': [88, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 5], [2, -5]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 4], [-2, -4]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 63272887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 176, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 22, 'label': '176.33.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.33', 'subgroup_hash': 33, 'subgroup_order': 176, 'subgroup_tex': 'Q_8\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 88, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 88, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 88, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.c1', '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': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 88, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': True, 'core_order': 88, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.10', 'subgroup_hash': 10, 'subgroup_order': 88, 'subgroup_tex': 'Q_8\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 44, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 63272888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 44, 'counter': 10, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 63272889
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 44, 'counter': 11, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 63272890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 44, 'counter': 12, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.4.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.c1', '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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 63272891
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63272892
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63272893
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 44, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '176.33.4.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.c1', '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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63272894
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 22, 'counter': 16, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.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': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 63272895
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 22, 'counter': 17, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '176.33.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272896
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 22, 'counter': 18, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '176.33.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 63272897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '176.33.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11.a1.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 2}
  • id: 63272899
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': True, 'core_order': 11, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '176.33.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.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': True, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 63272900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 44, 'characteristic': True, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '176.33.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.b1.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': 22, 'quotient_simple': 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: 63272902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.b1.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': 22, 'quotient_simple': 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: 63272903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.b1.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': 22, 'quotient_simple': 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: 63272904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.c1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.22.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.c1.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63272907
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', '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: 63272908
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.44.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', '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: 63272910
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.44.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', '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: 63272911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176.33.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.b1.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': 44, 'quotient_simple': 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: 63272912
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '176.33.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': 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: 63272913
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '176.33.44.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.c1.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': 44, 'quotient_simple': 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: 63272914
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '176.33.44.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.c1.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': 44, 'quotient_simple': 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: 63272915
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 2, 'counter': 35, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '176.33.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{22}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 63272916
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '176.33.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.b1.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': 88, '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: 63272917
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '176.33.88.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.b1.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': 88, '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: 63272918
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '176.33', 'ambient_counter': 33, 'ambient_order': 176, 'ambient_tex': 'Q_8\\times D_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 176, 'characteristic': True, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '176.33.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '176.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '176.33', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 33, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C5'], '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: 63272887
    {'ambient': '176.33', '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': '88.a1.a1', 'complements': ['176.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.a1.c1', '2.b1.a1', '2.b1.b1', '2.b1.c1', '2.c1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7712, 4999, 3831, 5226, 5253, 5000, 4484, 4995], 'generators': [1, 44, 88, 2, 16], 'label': '176.33.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.a1.c1', '2.b1.a1', '2.b1.b1', '2.b1.c1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 63272888
    {'ambient': '176.33', 'aut_centralizer_order': 88, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '20.5', 'aut_weyl_index': 264, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '44.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 6535, 6894, 7132, 4106, 6442, 895, 5577], 'generators': [44, 88, 16], 'label': '176.33.4.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', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '88.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272889
    {'ambient': '176.33', 'aut_centralizer_order': 88, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '20.5', 'aut_weyl_index': 264, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.a1', '44.a1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 6535, 637, 8014, 4106, 6442, 4002, 7663], 'generators': [1, 88, 16], 'label': '176.33.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '44.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '88.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272890
    {'ambient': '176.33', 'aut_centralizer_order': 88, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '20.5', 'aut_weyl_index': 264, 'centralizer': '4.b1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '2.b1.c1', '2.c1.a1'], 'contains': ['8.a1.a1', '44.a1.c1'], 'core': '4.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 6535, 3708, 5045, 4106, 6442, 1528, 8546], 'generators': [45, 88, 16], 'label': '176.33.4.b1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.c1', 'normal_contained_in': ['2.a1.c1', '2.b1.c1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '44.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.c1', 'projective_image': '88.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272891
    {'ambient': '176.33', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '220.7', 'aut_weyl_index': 24, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.c1'], 'contains': ['8.a1.a1', '44.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 4116, 4948, 4002, 2352, 4023, 2276, 4534], 'generators': [6, 16, 88], 'label': '176.33.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '88.11', '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': '44.3'}
  • id: 63272892
    {'ambient': '176.33', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '220.7', 'aut_weyl_index': 24, 'centralizer': '44.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.b1.c1'], 'contains': ['8.a1.a1', '44.c1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 4116, 2470, 2809, 2352, 4023, 5268, 3340], 'generators': [3, 16, 88], 'label': '176.33.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.b1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '88.11', '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': '44.3'}
  • id: 63272893
    {'ambient': '176.33', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '220.7', 'aut_weyl_index': 24, 'centralizer': '44.a1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '44.c1.c1'], 'core': '4.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 4116, 5986, 6089, 2352, 4023, 6124, 6620], 'generators': [7, 16, 88], 'label': '176.33.4.c1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.c1', 'normal_contained_in': ['2.a1.c1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.c1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.c1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 63272894
    {'ambient': '176.33', 'aut_centralizer_order': 528, 'aut_label': '8.a1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 528, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.c1.a1', '4.c1.b1', '4.c1.c1'], 'contains': ['16.a1.a1', '88.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3230, 4116, 5436, 5045, 2352, 4023, 2736, 5577], 'generators': [88, 16], 'label': '176.33.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.c1.b1', '4.c1.c1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272895
    {'ambient': '176.33', 'aut_centralizer_order': 24, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 48, 'centralizer': '22.a1.a1', 'complements': ['22.a1.a1', '22.c1.a1', '22.c1.b1', '22.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '88.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1169, 1884, 8709, 2147, 852, 1791, 2096, 4313], 'generators': [2, 16], 'label': '176.33.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '176.33', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 63272896
    {'ambient': '176.33', 'aut_centralizer_order': 24, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 48, 'centralizer': '22.a1.a1', 'complements': ['22.a1.a1', '22.c1.a1', '22.c1.b1', '22.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '88.b1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1169, 1884, 9485, 3781, 852, 1791, 1456, 2678], 'generators': [90, 16], 'label': '176.33.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '176.33', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 63272897
    {'ambient': '176.33', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.48', 'aut_weyl_index': 110, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.b1.b1', '22.b1.c1', '22.c1.a1', '22.c1.b1', '22.c1.c1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9010, -1, 2548, -1, 8997, -1, 7793, -1], 'generators': [1, 2, 44], 'label': '176.33.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272898
    {'ambient': '176.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '440.42', 'aut_weyl_index': 12, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 1697, 8053, 3581, 1661, 1698, 593, 732], 'generators': [2, 88, 16, 44], 'label': '176.33.2.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.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '88.11', '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': '44.3'}
  • id: 63272899
    {'ambient': '176.33', 'aut_centralizer_order': 528, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 528, 'centralizer': '2.c1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [568, 3233, 9207, 4273, 1779, 3093, 2140, 4945], 'generators': [16], 'label': '176.33.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '176.33', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272900
    {'ambient': '176.33', 'aut_centralizer_order': 220, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 220, 'centralizer': '4.a1.a1', 'complements': ['8.b1.a1', '8.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.a1.b1', '44.a1.c1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9432, 8047, 1754, 7343, 8963, 8302, 4578, 9348], 'generators': [1, 44], 'label': '176.33.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['44.a1.a1', '44.a1.b1', '44.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272901
    {'ambient': '176.33', 'aut_centralizer_order': 40, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1320, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5569, -1, 6727, -1, 5995, -1, 3197, -1], 'generators': [2, 44], 'label': '176.33.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272902
    {'ambient': '176.33', 'aut_centralizer_order': 40, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1320, 'centralizer': '22.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '11.a1.a1'], 'contains': ['44.a1.b1', '44.b1.a1', '44.c1.b1'], 'core': '44.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5569, -1, 515, -1, 5995, -1, 8540, -1], 'generators': [1, 2], 'label': '176.33.22.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.b1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272903
    {'ambient': '176.33', 'aut_centralizer_order': 40, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1320, 'centralizer': '22.b1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '11.a1.a1'], 'contains': ['44.a1.c1', '44.b1.a1', '44.c1.c1'], 'core': '44.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [5569, -1, 5210, -1, 5995, -1, 7044, -1], 'generators': [45, 2], 'label': '176.33.22.b1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.c1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272904
    {'ambient': '176.33', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 660, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.c1.b1', '44.c1.c1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7873, -1, 3971, -1, 7749, -1, 9806, -1], 'generators': [3, 44], 'label': '176.33.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272905
    {'ambient': '176.33', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 660, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '11.a1.a1'], 'contains': ['44.a1.b1', '44.c1.a1', '44.c1.c1'], 'core': '44.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [7873, -1, 3010, -1, 7749, -1, 9289, -1], 'generators': [1, 6], 'label': '176.33.22.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.b1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272906
    {'ambient': '176.33', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 660, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.c1', '11.a1.a1'], 'contains': ['44.a1.c1', '44.c1.a1', '44.c1.b1'], 'core': '44.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [7873, -1, 2382, -1, 7749, -1, 7793, -1], 'generators': [45, 6], 'label': '176.33.22.c1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.c1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63272907
    {'ambient': '176.33', 'aut_centralizer_order': 880, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.a1.a1', '22.b1.a1', '22.c1.a1'], 'contains': ['88.a1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6980, 6535, 5541, 6701, 6298, 6442, 4060, 6660], 'generators': [44], 'label': '176.33.44.a1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.b1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272908
    {'ambient': '176.33', 'aut_centralizer_order': 880, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '22.a1.a1', '22.b1.b1', '22.c1.b1'], 'contains': ['88.a1.a1'], 'core': '44.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6980, 6535, 1754, 7422, 6298, 6442, 5613, 7663], 'generators': [1], 'label': '176.33.44.a1.b1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.b1', 'normal_contained_in': ['4.b1.b1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.b1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272909
    {'ambient': '176.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '440.42', 'aut_weyl_index': 12, 'centralizer': '44.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1', '22.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 1697, 637, 733, 1661, 1698, 4995, 2377], 'generators': [1, 88, 16, 2], 'label': '176.33.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 63272910
    {'ambient': '176.33', 'aut_centralizer_order': 880, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '2.a1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.c1', '22.a1.a1', '22.b1.c1', '22.c1.c1'], 'contains': ['88.a1.a1'], 'core': '44.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6980, 6535, 3491, 5897, 6298, 6442, 4578, 8546], 'generators': [45], 'label': '176.33.44.a1.c1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.c1', 'normal_contained_in': ['4.b1.c1', '22.a1.a1'], 'normal_contains': ['88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.c1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.1', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.a1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272911
    {'ambient': '176.33', 'aut_centralizer_order': 240, 'aut_label': '44.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.b1.a1', '22.b1.b1', '22.b1.c1'], 'contains': ['88.a1.a1', '88.b1.a1', '88.b1.b1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2566, -1, 7958, -1, 3786, -1, 3348, -1], 'generators': [2, 88], 'label': '176.33.44.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63272912
    {'ambient': '176.33', 'aut_centralizer_order': 80, 'aut_label': '44.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1', '22.c1.b1', '22.c1.c1'], 'contains': ['88.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5000, -1, 4285, -1, 5084, -1, 5095, -1], 'generators': [6], 'label': '176.33.44.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272913
    {'ambient': '176.33', 'aut_centralizer_order': 80, 'aut_label': '44.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '22.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '22.b1.b1', '22.c1.a1', '22.c1.c1'], 'contains': ['88.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5000, -1, 2382, -1, 5084, -1, 7159, -1], 'generators': [3], 'label': '176.33.44.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.c1.b1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272914
    {'ambient': '176.33', 'aut_centralizer_order': 80, 'aut_label': '44.c1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2640, 'centralizer': '22.b1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.c1', '22.b1.c1', '22.c1.a1', '22.c1.b1'], 'contains': ['88.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5000, -1, 4913, -1, 5084, -1, 7677, -1], 'generators': [7], 'label': '176.33.44.c1.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.c1.c1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.c1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63272915
    {'ambient': '176.33', 'aut_centralizer_order': 5280, 'aut_label': '88.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5280, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1', '44.a1.b1', '44.a1.c1', '44.b1.a1', '44.c1.a1', '44.c1.b1', '44.c1.c1'], 'contains': ['176.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3539, 4698, 4913, 5897, 4342, 4953, 4578, 6660], 'generators': [88], 'label': '176.33.88.a1.a1', 'mobius_quo': -1, 'mobius_sub': 88, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.a1.a1', '44.a1.a1', '44.a1.b1', '44.a1.c1'], 'normal_contains': ['176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '88.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '88.11', 'quotient_action_kernel_order': 88, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63272916
    {'ambient': '176.33', 'aut_centralizer_order': 240, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5280, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.b1.a1'], 'contains': ['176.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2127, -1, 8167, -1, 3128, -1, 3269, -1], 'generators': [2], 'label': '176.33.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.b1.a1', 'projective_image': '176.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63272917
    {'ambient': '176.33', 'aut_centralizer_order': 240, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5280, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '44.b1.a1'], 'contains': ['176.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2127, -1, 8796, -1, 3128, -1, 2751, -1], 'generators': [90], 'label': '176.33.88.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.b1.b1', 'projective_image': '176.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63272918
    {'ambient': '176.33', 'aut_centralizer_order': None, 'aut_label': '176.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': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.b1.b1'], 'contains': [], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2127, 4024, 8481, 5437, 3128, 4023, 3010, 5346], 'generators': [], 'label': '176.33.176.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '176.a1.a1', 'normal_contained_in': ['16.a1.a1', '88.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '176.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63272919
    {'ambient': '176.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '440.42', 'aut_weyl_index': 12, 'centralizer': '44.a1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.c1', '4.c1.c1', '22.b1.c1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 1697, 6623, 5226, 1661, 1698, 2952, 6419], 'generators': [45, 88, 16, 2], 'label': '176.33.2.a1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.c1', '4.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.c1', 'projective_image': '88.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.c1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 63272920
    {'ambient': '176.33', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 6, 'centralizer': '88.a1.a1', 'complements': ['88.b1.a1', '88.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.c1.c1', '22.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 4999, 5384, 6650, 4056, 5000, 6872, 3801], 'generators': [3, 88, 16, 44], 'label': '176.33.2.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.c1.b1', '4.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '88.11', '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': '88.11'}
  • id: 63272921
    {'ambient': '176.33', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 6, 'centralizer': '88.a1.a1', 'complements': ['88.b1.a1', '88.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.c1.c1', '22.c1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 4999, 4345, 7843, 4056, 5000, 6016, 7844], 'generators': [1, 88, 16, 6], 'label': '176.33.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.c1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
  • id: 63272922
    {'ambient': '176.33', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 6, 'centralizer': '88.a1.a1', 'complements': ['88.b1.a1', '88.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.c1', '4.c1.a1', '4.c1.b1', '22.c1.c1'], 'core': '2.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 4999, 3307, 2157, 4056, 5000, 3973, 4995], 'generators': [45, 88, 16, 6], 'label': '176.33.2.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.c1', '4.c1.b1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.c1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.c1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
  • id: 63272923
    {'ambient': '176.33', 'aut_centralizer_order': 22, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '240.196', 'aut_weyl_index': 22, 'centralizer': '8.a1.a1', 'complements': ['88.b1.a1', '88.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.b1.c1', '22.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8864, 8303, 2068, 9267, 6450, 8302, 1773, 9268], 'generators': [1, 16, 88, 44], 'label': '176.33.2.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.b1.b1', '4.b1.c1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '88.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63272924
    {'ambient': '176.33', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 24, 'centralizer': '22.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.a1.c1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '44.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2386, 1697, 8334, 1766, 599, 1605, 255, 2297], 'generators': [2, 16, 88], 'label': '176.33.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.a1.c1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '88.11', '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': '22.1'}