Abstract group data - 990.16

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 1320, 'aut_gen_orders': [2, 30, 4, 4, 3, 33], 'aut_gens': [[1, 10, 30], [1, 20, 300], [661, 340, 390], [1, 340, 710], [1, 660, 380], [331, 10, 30], [711, 10, 30]], 'aut_group': '47520.b', 'aut_hash': 4147157100757437592, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 47520, 'aut_permdeg': 20, 'aut_perms': [1808195308132965210, 1471408994146687380, 102126948835743801, 43794270459291319, 43441247281795503, 1043438637957603724], 'aut_phi_ratio': 198.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 4, 1], [5, 11, 1, 4], [10, 99, 1, 4], [11, 5, 2, 1], [15, 22, 4, 4], [22, 45, 2, 1], [33, 10, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}\\times C_3^2:\\GL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '47520.b', 'autcentquo_hash': 4147157100757437592, 'autcentquo_nilpotent': False, 'autcentquo_order': 47520, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 2, 4], [5, 11, 4], [10, 99, 4], [11, 5, 2], [15, 22, 16], [22, 45, 2], [33, 10, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '990.16', 'commutator_count': 1, 'commutator_label': '99.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 1], ['55.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 1, 4], [5, 11, 4, 1], [10, 99, 4, 1], [11, 5, 2, 1], [15, 22, 4, 4], [22, 45, 2, 1], [33, 10, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10416, 'exponent': 330, 'exponents_of_order': [2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '990.16', 'hash': 16, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [10, 3, 33], 'inner_gens': [[1, 20, 780], [21, 10, 30], [241, 10, 30]], 'inner_hash': 16, 'inner_nilpotent': False, 'inner_order': 990, 'inner_split': False, 'inner_tex': '(C_3\\times C_{33}):C_{10}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 10], [2, 20], [5, 4], [10, 8]], 'label': '990.16', 'linC_count': 600, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 12, 'linQ_dim': 14, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C3*C33):C10', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 42, 'number_divisions': 18, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 48, 'number_subgroups': 392, 'old_label': None, 'order': 990, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 9], [3, 8], [5, 44], [10, 396], [11, 10], [15, 352], [22, 90], [33, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [0, 10, 5, 675, 5], 'outer_gens': [[1, 10, 980], [11, 10, 300], [1, 20, 710], [331, 330, 370], [1, 350, 50]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [143, 127, 576, 126, 121], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 4], [4, 2], [8, 4], [10, 2], [20, 4]], 'representations': {'PC': {'code': 6177879569382695549514503119, 'gens': [1, 3, 4], 'pres': [5, -2, -5, -3, -3, -11, 10, 302, 15603, 4808, 78, 9004, 5634]}, 'GLZN': {'d': 2, 'p': 66, 'gens': [287521, 433456, 12366023, 287893, 288949]}, 'Perm': {'d': 17, 'gens': [25, 1496082031920, 144, 243, 23733216460800]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_{33}):C_{10}', 'transitive_degree': 99, '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: 144062582
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 16, 'group_order': 990, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 144062593
    {'aut_label': '2A', 'centralizer': '9.a1.a1', 'counter': 2, 'group_counter': 16, 'group_order': 990, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 335, 'size': 9}
  • id: 144062604
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 16, 'group_order': 990, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3], 'representative': 330, 'size': 2}
  • id: 144062615
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 4, 'group_counter': 16, 'group_order': 990, 'label': '3B', 'order': 3, 'powers': [4, 1, 4, 4], 'representative': 20, 'size': 2}
  • id: 144062619
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 16, 'group_order': 990, 'label': '3C', 'order': 3, 'powers': [5, 1, 5, 5], 'representative': 350, 'size': 2}
  • id: 144062620
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 16, 'group_order': 990, 'label': '3D', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 680, 'size': 2}
  • id: 144062621
    {'aut_label': '5A1', 'centralizer': '11.a1.a1', 'counter': 7, 'group_counter': 16, 'group_order': 990, 'label': '5A1', 'order': 5, 'powers': [9, 10, 1, 7], 'representative': 276, 'size': 11}
  • id: 144062622
    {'aut_label': '5A-1', 'centralizer': '11.a1.a1', 'counter': 8, 'group_counter': 16, 'group_order': 990, 'label': '5A-1', 'order': 5, 'powers': [10, 9, 1, 8], 'representative': 184, 'size': 11}
  • id: 144062623
    {'aut_label': '5A2', 'centralizer': '11.a1.a1', 'counter': 9, 'group_counter': 16, 'group_order': 990, 'label': '5A2', 'order': 5, 'powers': [8, 7, 1, 9], 'representative': 362, 'size': 11}
  • id: 144062583
    {'aut_label': '5A-2', 'centralizer': '11.a1.a1', 'counter': 10, 'group_counter': 16, 'group_order': 990, 'label': '5A-2', 'order': 5, 'powers': [7, 8, 1, 10], 'representative': 728, 'size': 11}
  • id: 144062584
    {'aut_label': '10A1', 'centralizer': '99.a1.a1', 'counter': 11, 'group_counter': 16, 'group_order': 990, 'label': '10A1', 'order': 10, 'powers': [7, 13, 2, 11], 'representative': 953, 'size': 99}
  • id: 144062585
    {'aut_label': '10A-1', 'centralizer': '99.a1.a1', 'counter': 12, 'group_counter': 16, 'group_order': 990, 'label': '10A-1', 'order': 10, 'powers': [8, 14, 2, 12], 'representative': 327, 'size': 99}
  • id: 144062586
    {'aut_label': '10A3', 'centralizer': '99.a1.a1', 'counter': 13, 'group_counter': 16, 'group_order': 990, 'label': '10A3', 'order': 10, 'powers': [10, 12, 2, 13], 'representative': 509, 'size': 99}
  • id: 144062587
    {'aut_label': '10A-3', 'centralizer': '99.a1.a1', 'counter': 14, 'group_counter': 16, 'group_order': 990, 'label': '10A-3', 'order': 10, 'powers': [9, 11, 2, 14], 'representative': 411, 'size': 99}
  • id: 144062588
    {'aut_label': '11A1', 'centralizer': '5.a1.a1', 'counter': 15, 'group_counter': 16, 'group_order': 990, 'label': '11A1', 'order': 11, 'powers': [16, 15, 15, 1], 'representative': 90, 'size': 5}
  • id: 144062589
    {'aut_label': '11A1', 'centralizer': '5.a1.a1', 'counter': 16, 'group_counter': 16, 'group_order': 990, 'label': '11A-1', 'order': 11, 'powers': [15, 16, 16, 1], 'representative': 900, 'size': 5}
  • id: 144062590
    {'aut_label': '15A1', 'centralizer': '22.a1.a1', 'counter': 17, 'group_counter': 16, 'group_order': 990, 'label': '15A1', 'order': 15, 'powers': [19, 7, 3, 17], 'representative': 32, 'size': 22}
  • id: 144062591
    {'aut_label': '15A-1', 'centralizer': '22.a1.a1', 'counter': 18, 'group_counter': 16, 'group_order': 990, 'label': '15A-1', 'order': 15, 'powers': [20, 8, 3, 18], 'representative': 38, 'size': 22}
  • id: 144062592
    {'aut_label': '15A2', 'centralizer': '22.a1.a1', 'counter': 19, 'group_counter': 16, 'group_order': 990, 'label': '15A2', 'order': 15, 'powers': [18, 9, 3, 19], 'representative': 34, 'size': 22}
  • id: 144062594
    {'aut_label': '15A-2', 'centralizer': '22.a1.a1', 'counter': 20, 'group_counter': 16, 'group_order': 990, 'label': '15A-2', 'order': 15, 'powers': [17, 10, 3, 20], 'representative': 36, 'size': 22}
  • id: 144062595
    {'aut_label': '15A1', 'centralizer': '22.a1.a1', 'counter': 21, 'group_counter': 16, 'group_order': 990, 'label': '15B1', 'order': 15, 'powers': [23, 7, 4, 21], 'representative': 12, 'size': 22}
  • id: 144062596
    {'aut_label': '15A-1', 'centralizer': '22.a1.a1', 'counter': 22, 'group_counter': 16, 'group_order': 990, 'label': '15B-1', 'order': 15, 'powers': [24, 8, 4, 22], 'representative': 18, 'size': 22}
  • id: 144062597
    {'aut_label': '15A2', 'centralizer': '22.a1.a1', 'counter': 23, 'group_counter': 16, 'group_order': 990, 'label': '15B2', 'order': 15, 'powers': [22, 9, 4, 23], 'representative': 14, 'size': 22}
  • id: 144062598
    {'aut_label': '15A-2', 'centralizer': '22.a1.a1', 'counter': 24, 'group_counter': 16, 'group_order': 990, 'label': '15B-2', 'order': 15, 'powers': [21, 10, 4, 24], 'representative': 16, 'size': 22}
  • id: 144062599
    {'aut_label': '15A1', 'centralizer': '22.a1.a1', 'counter': 25, 'group_counter': 16, 'group_order': 990, 'label': '15C1', 'order': 15, 'powers': [27, 7, 5, 25], 'representative': 42, 'size': 22}
  • id: 144062600
    {'aut_label': '15A-1', 'centralizer': '22.a1.a1', 'counter': 26, 'group_counter': 16, 'group_order': 990, 'label': '15C-1', 'order': 15, 'powers': [28, 8, 5, 26], 'representative': 48, 'size': 22}
  • id: 144062601
    {'aut_label': '15A2', 'centralizer': '22.a1.a1', 'counter': 27, 'group_counter': 16, 'group_order': 990, 'label': '15C2', 'order': 15, 'powers': [26, 9, 5, 27], 'representative': 44, 'size': 22}
  • id: 144062602
    {'aut_label': '15A-2', 'centralizer': '22.a1.a1', 'counter': 28, 'group_counter': 16, 'group_order': 990, 'label': '15C-2', 'order': 15, 'powers': [25, 10, 5, 28], 'representative': 46, 'size': 22}
  • id: 144062603
    {'aut_label': '15A1', 'centralizer': '22.a1.a1', 'counter': 29, 'group_counter': 16, 'group_order': 990, 'label': '15D1', 'order': 15, 'powers': [31, 7, 6, 29], 'representative': 72, 'size': 22}
  • id: 144062605
    {'aut_label': '15A-1', 'centralizer': '22.a1.a1', 'counter': 30, 'group_counter': 16, 'group_order': 990, 'label': '15D-1', 'order': 15, 'powers': [32, 8, 6, 30], 'representative': 78, 'size': 22}
  • id: 144062606
    {'aut_label': '15A2', 'centralizer': '22.a1.a1', 'counter': 31, 'group_counter': 16, 'group_order': 990, 'label': '15D2', 'order': 15, 'powers': [30, 9, 6, 31], 'representative': 74, 'size': 22}
  • id: 144062607
    {'aut_label': '15A-2', 'centralizer': '22.a1.a1', 'counter': 32, 'group_counter': 16, 'group_order': 990, 'label': '15D-2', 'order': 15, 'powers': [29, 10, 6, 32], 'representative': 76, 'size': 22}
  • id: 144062608
    {'aut_label': '22A1', 'centralizer': '45.a1.a1', 'counter': 33, 'group_counter': 16, 'group_order': 990, 'label': '22A1', 'order': 22, 'powers': [15, 33, 33, 2], 'representative': 245, 'size': 45}
  • id: 144062609
    {'aut_label': '22A1', 'centralizer': '45.a1.a1', 'counter': 34, 'group_counter': 16, 'group_order': 990, 'label': '22A-1', 'order': 22, 'powers': [16, 34, 34, 2], 'representative': 425, 'size': 45}
  • id: 144062610
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 35, 'group_counter': 16, 'group_order': 990, 'label': '33A1', 'order': 33, 'powers': [36, 15, 35, 3], 'representative': 30, 'size': 10}
  • id: 144062611
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 36, 'group_counter': 16, 'group_order': 990, 'label': '33A-1', 'order': 33, 'powers': [35, 16, 36, 3], 'representative': 60, 'size': 10}
  • id: 144062612
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 37, 'group_counter': 16, 'group_order': 990, 'label': '33B1', 'order': 33, 'powers': [38, 15, 37, 4], 'representative': 100, 'size': 10}
  • id: 144062613
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 38, 'group_counter': 16, 'group_order': 990, 'label': '33B-1', 'order': 33, 'powers': [37, 16, 38, 4], 'representative': 190, 'size': 10}
  • id: 144062614
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 39, 'group_counter': 16, 'group_order': 990, 'label': '33C1', 'order': 33, 'powers': [40, 15, 39, 5], 'representative': 40, 'size': 10}
  • id: 144062616
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 40, 'group_counter': 16, 'group_order': 990, 'label': '33C-1', 'order': 33, 'powers': [39, 16, 40, 5], 'representative': 80, 'size': 10}
  • id: 144062617
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 41, 'group_counter': 16, 'group_order': 990, 'label': '33D1', 'order': 33, 'powers': [42, 16, 41, 6], 'representative': 70, 'size': 10}
  • id: 144062618
    {'aut_label': '33A1', 'centralizer': '10.a1.a1', 'counter': 42, 'group_counter': 16, 'group_order': 990, 'label': '33D-1', 'order': 33, 'powers': [41, 15, 42, 6], 'representative': 50, 'size': 10}
• 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: 13996949
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13996959
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13996962
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13996963
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, -1, -1, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, 2, -1, 2, -1, -1], 'schur_index': 1}
  • id: 13996964
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, -1, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 13996965
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 0, 0, 2, -1, -1, -1, 2, -1, -1, -1], 'schur_index': 1}
  • id: 13996960
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.1c', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 13996961
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.1d', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, -1, -1, -1, -1, 1, 1, 1, 1, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 13996966
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2e', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 0, -4, -4, -4, 8, -2, -2, -2, -2, 0, 0, 0, 0, 8, 8, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 0, 0, -4, 8, 8, -4, -4, -4, -4, -4], 'schur_index': 1}
  • id: 13996950
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2f', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 0, -4, -4, 8, -4, -2, -2, -2, -2, 0, 0, 0, 0, 8, 8, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, -4, -4, -4, 8, -4, 8, -4, -4], 'schur_index': 1}
  • id: 13996951
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2g', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 0, -4, 8, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 8, 8, 1, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 0, 0, -4, -4, -4, -4, -4, -4, 8, 8], 'schur_index': 1}
  • id: 13996952
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.2h', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 0, 8, -4, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 8, 8, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 0, 0, 8, -4, -4, -4, 8, -4, -4, -4], 'schur_index': 1}
  • id: 13996953
    {'cdim': 5, 'counter': 13, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.5a', 'multiplicity': 2, 'nt': [11, 3], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13996954
    {'cdim': 5, 'counter': 14, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.5b', 'multiplicity': 2, 'nt': [22, 5], 'qdim': 10, 'qvalues': [10, -10, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13996955
    {'cdim': 10, 'counter': 15, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.10a', 'multiplicity': 2, 'nt': [33, 7], 'qdim': 20, 'qvalues': [20, 0, -10, -10, -10, 20, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13996956
    {'cdim': 10, 'counter': 16, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.10b', 'multiplicity': 2, 'nt': [33, 7], 'qdim': 20, 'qvalues': [20, 0, -10, -10, 20, -10, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, -2, 1, 1], 'schur_index': 1}
  • id: 13996957
    {'cdim': 10, 'counter': 17, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.10c', 'multiplicity': 2, 'nt': [33, 7], 'qdim': 20, 'qvalues': [20, 0, -10, 20, -10, -10, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 13996958
    {'cdim': 10, 'counter': 18, 'faithful': False, 'group': '990.16', 'group_order': 990, 'image': None, 'label': '990.16.10d', 'multiplicity': 2, 'nt': [33, 7], 'qdim': 20, 'qvalues': [20, 0, 20, -10, -10, -10, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 33155348
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 990, 'label': '990.16.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155359
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 495, 'label': '990.16.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155370
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 3, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 198, 'label': '990.16.1c1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155381
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 4, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 198, 'label': '990.16.1c2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155385
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 198, 'label': '990.16.1c3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155386
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 198, 'label': '990.16.1c4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155387
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 99, 'label': '990.16.1d1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155388
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 99, 'label': '990.16.1d2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155389
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 99, 'label': '990.16.1d3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155349
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 990, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 99, 'label': '990.16.1d4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33155350
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 165, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 165, 'label': '990.16.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155351
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  • id: 33155352
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  • id: 33155353
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  • id: 33155354
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  • id: 33155355
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  • id: 33155356
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 165, 'counter': 17, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.b1', 'kernel_order': 33, 'label': '990.16.2e3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[2, 1]], [[2, -1]], [[2, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[2, -2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155357
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 165, 'counter': 18, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.b1', 'kernel_order': 33, 'label': '990.16.2e4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155358
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 165, 'counter': 19, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 33, 'label': '990.16.2f1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155360
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 165, 'counter': 20, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 33, 'label': '990.16.2f2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155361
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  • id: 33155362
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 165, 'counter': 22, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 33, 'label': '990.16.2f4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -2]], [[2, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155363
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  • id: 33155364
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  • id: 33155365
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  • id: 33155366
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  • id: 33155367
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  • id: 33155368
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 165, 'counter': 28, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.c1', 'kernel_order': 33, 'label': '990.16.2h2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[2, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[2, -2]], [[2, 2]], [[2, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155369
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  • id: 33155371
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 165, 'counter': 30, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.c1', 'kernel_order': 33, 'label': '990.16.2h4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[2, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[2, -1]], [[2, 1]], [[2, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33155372
    {'center': '55.a1.a1', 'center_index': 55, 'center_order': 18, 'counter': 31, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '55.1', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 18, 'label': '990.16.5a1', 'nt': [11, 3], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 33155373
    {'center': '55.a1.a1', 'center_index': 55, 'center_order': 18, 'counter': 32, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '55.1', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 18, 'label': '990.16.5a2', 'nt': [11, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 33155374
    {'center': '55.a1.a1', 'center_index': 55, 'center_order': 18, 'counter': 33, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '110.2', 'image_order': 110, 'indicator': 0, 'kernel': '110.a1.a1', 'kernel_order': 9, 'label': '990.16.5b1', 'nt': [22, 5], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 33155375
    {'center': '55.a1.a1', 'center_index': 55, 'center_order': 18, 'counter': 34, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '110.2', 'image_order': 110, 'indicator': 0, 'kernel': '110.a1.a1', 'kernel_order': 9, 'label': '990.16.5b2', 'nt': [22, 2], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 33155376
    {'center': '330.a1.b1', 'center_index': 330, 'center_order': 3, 'counter': 35, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.b1', 'kernel_order': 3, 'label': '990.16.10a1', 'nt': [33, 7], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 33155377
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  • id: 33155378
    {'center': '330.a1.a1', 'center_index': 330, 'center_order': 3, 'counter': 37, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.a1', 'kernel_order': 3, 'label': '990.16.10b1', 'nt': [33, 7], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 33155379
    {'center': '330.a1.a1', 'center_index': 330, 'center_order': 3, 'counter': 38, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.a1', 'kernel_order': 3, 'label': '990.16.10b2', 'nt': [33, 2], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 33155380
    {'center': '330.a1.d1', 'center_index': 330, 'center_order': 3, 'counter': 39, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.d1', 'kernel_order': 3, 'label': '990.16.10c1', 'nt': [33, 7], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[-5, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]]]}
  • id: 33155382
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  • id: 33155383
    {'center': '330.a1.c1', 'center_index': 330, 'center_order': 3, 'counter': 41, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.c1', 'kernel_order': 3, 'label': '990.16.10d1', 'nt': [33, 7], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 33155384
    {'center': '330.a1.c1', 'center_index': 330, 'center_order': 3, 'counter': 42, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [3, -1, 1], 'group': '990.16', 'group_counter': 16, 'group_order': 990, 'image': None, 'image_isoclass': '330.2', 'image_order': 330, 'indicator': 0, 'kernel': '330.a1.c1', 'kernel_order': 3, 'label': '990.16.10d2', 'nt': [33, 2], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[10, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
• 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: 115755274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 990, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 330, 'label': '990.16.1.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': '990.16', 'subgroup_hash': 16, 'subgroup_order': 990, 'subgroup_tex': '(C_3\\times C_{33}):C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 495, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 165, 'label': '990.16.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '495.3', 'subgroup_hash': 3, 'subgroup_order': 495, 'subgroup_tex': 'C_{33}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755296
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 165, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.2', 'subgroup_hash': 2, 'subgroup_order': 330, 'subgroup_tex': 'C_{33}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755307
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 165, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.2', 'subgroup_hash': 2, 'subgroup_order': 330, 'subgroup_tex': 'C_{33}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755317
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 165, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.3.a1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.2', 'subgroup_hash': 2, 'subgroup_order': 330, 'subgroup_tex': 'C_{33}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755318
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 165, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.3.a1.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.2', 'subgroup_hash': 2, 'subgroup_order': 330, 'subgroup_tex': 'C_{33}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': True, 'core_order': 198, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 66, 'label': '990.16.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '198.8', 'subgroup_hash': 8, 'subgroup_order': 198, 'subgroup_tex': 'C_{33}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755320
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 165, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '990.16.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755321
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 165, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '990.16.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755275
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 165, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '990.16.6.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755276
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 165, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '990.16.6.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755277
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 55, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 110, 'label': '990.16.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755278
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 99, 'characteristic': True, 'core_order': 99, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 33, 'label': '990.16.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '99.2', 'subgroup_hash': 2, 'subgroup_order': 99, 'subgroup_tex': 'C_3\\times C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 115755279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 18, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '990.16.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755280
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 33, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 115755281
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 33, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.15.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 115755282
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 33, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.15.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 115755283
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 33, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.15.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.1', 'subgroup_hash': 1, 'subgroup_order': 66, 'subgroup_tex': 'S_3\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 115755284
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 18, 'characteristic': True, 'core_order': 55, 'counter': 19, 'cyclic': False, 'direct': True, 'hall': 55, 'label': '990.16.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 115755286
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 9, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 15, 'label': '990.16.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 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': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755287
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 99, 'characteristic': False, 'core_order': 33, 'counter': 21, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 115755288
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 99, 'characteristic': False, 'core_order': 33, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.30.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 115755289
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 99, 'characteristic': False, 'core_order': 33, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.30.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 115755290
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 99, 'characteristic': False, 'core_order': 33, 'counter': 24, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.30.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 115755291
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755292
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.33.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.a1.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755293
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.33.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.a1.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755294
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.33.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755295
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 11, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 22, 'label': '990.16.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 115755297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 55, 'characteristic': True, 'core_order': 18, 'counter': 30, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '990.16.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755298
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '990.16.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755299
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '990.16.66.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.a1.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755300
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '990.16.66.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.a1.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '990.16.66.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 115755302
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 198, 'characteristic': True, 'core_order': 11, 'counter': 35, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '990.16.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '90.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 90, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:S_3', 'simple': True, 'solvable': True, 'special_labels': ['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: 115755303
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 10, 'label': '990.16.99.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '99.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': 99, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 115755304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 495, 'characteristic': True, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '990.16.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 115755305
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 3, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.165.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.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': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755306
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.165.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.a1.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': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755308
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 3, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.165.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.a1.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': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755309
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 3, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '990.16.165.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755310
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '990.16.198.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 115755311
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 495, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.330.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '330.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '330.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 330, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{33}:C_{10}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755312
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 495, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.330.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '330.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '330.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 330, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{33}:C_{10}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755313
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 495, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.330.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '330.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '330.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 330, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{33}:C_{10}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755314
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 495, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '990.16.330.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '330.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '330.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 330, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{33}:C_{10}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115755315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 110, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '990.16.495.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '495.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': 495, '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': 2}
  • id: 115755316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '990.16', 'ambient_counter': 16, 'ambient_order': 990, 'ambient_tex': '(C_3\\times C_{33}):C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 990, 'characteristic': True, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '990.16.990.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '990.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '990.16', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 990, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_3\\times C_{33}):C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', '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: 115755274
    {'ambient': '990.16', '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': '990.a1.a1', 'complements': ['990.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.a1.b1', '3.a1.c1', '3.a1.d1', '5.a1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3431, 3322, 6110, 3213, 6108, 4402, 5462, 6548], 'generators': [5, 10, 660, 2, 90], 'label': '990.16.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '990.16', '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': '990.16'}
  • id: 115755275
    {'ambient': '990.16', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 216, 'centralizer': '110.a1.a1', 'complements': ['165.a1.a1', '165.a1.d1', '165.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.c1'], 'contains': ['18.a1.a1', '30.a1.c1', '66.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 7007, 8294, 9115, 2598, 7956, 2618, 6618], 'generators': [670, 90, 2], 'label': '990.16.6.a1.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '30.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.c1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.2'}
  • id: 115755276
    {'ambient': '990.16', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 216, 'centralizer': '110.a1.a1', 'complements': ['165.a1.a1', '165.a1.b1', '165.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.d1'], 'contains': ['18.a1.a1', '30.a1.d1', '66.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 7007, 5919, 5187, 2598, 7956, 1102, 2785], 'generators': [340, 90, 2], 'label': '990.16.6.a1.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.d1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '30.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.d1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.d1', 'subgroup_fusion': None, 'weyl_group': '110.2'}
  • id: 115755277
    {'ambient': '990.16', 'aut_centralizer_order': 48, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '110.1', 'aut_weyl_index': 432, 'centralizer': '495.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.b1', '3.a1.c1', '3.a1.d1'], 'contains': ['18.a1.a1', '45.a1.a1', '99.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8760, -1, 7102, -1, 811, -1, 4653, -1], 'generators': [5, 90, 2], 'label': '990.16.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
  • id: 115755278
    {'ambient': '990.16', 'aut_centralizer_order': 99, 'aut_label': '10.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '480.1017', 'aut_weyl_index': 99, 'centralizer': '10.a1.a1', 'complements': ['99.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.a1.b1', '30.a1.c1', '30.a1.d1', '110.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1896, 4133, 1963, 2049, 8494, 3798, 3317, 8386], 'generators': [10, 90, 660], 'label': '990.16.10.a1.a1', 'mobius_quo': -3, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['30.a1.c1', '30.a1.d1', '30.a1.b1', '30.a1.a1', '110.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 115755279
    {'ambient': '990.16', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '432.734', 'aut_weyl_index': 110, 'centralizer': '198.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '33.a1.a1', '33.a1.b1', '33.a1.c1', '33.a1.d1', '55.a1.a1'], 'core': '55.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1656, -1, 8201, -1, 6993, -1, 7724, -1], 'generators': [5, 10, 660, 2], 'label': '990.16.11.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': '990.16', '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': '18.4'}
  • id: 115755280
    {'ambient': '990.16', 'aut_centralizer_order': 66, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '60.11', 'aut_weyl_index': 792, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '45.a1.a1', '165.a1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6542, -1, 1788, -1, 5491, -1, 5349, -1], 'generators': [5, 660, 90], 'label': '990.16.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.1'}
  • id: 115755281
    {'ambient': '990.16', 'aut_centralizer_order': 66, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '60.11', 'aut_weyl_index': 792, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1', '5.a1.a1'], 'contains': ['30.a1.b1', '45.a1.a1', '165.a1.b1'], 'core': '30.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6542, -1, 370, -1, 5491, -1, 6615, -1], 'generators': [5, 10, 90], 'label': '990.16.15.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '15.a1.b1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.b1', 'subgroup_fusion': None, 'weyl_group': '30.1'}
  • id: 115755282
    {'ambient': '990.16', 'aut_centralizer_order': 66, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '60.11', 'aut_weyl_index': 792, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.c1', '5.a1.a1'], 'contains': ['30.a1.c1', '45.a1.a1', '165.a1.c1'], 'core': '30.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6542, -1, 4430, -1, 5491, -1, 8306, -1], 'generators': [5, 670, 90], 'label': '990.16.15.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '15.a1.c1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.c1', 'subgroup_fusion': None, 'weyl_group': '30.1'}
  • id: 115755283
    {'ambient': '990.16', 'aut_centralizer_order': 66, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '60.11', 'aut_weyl_index': 792, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.d1', '5.a1.a1'], 'contains': ['30.a1.d1', '45.a1.a1', '165.a1.d1'], 'core': '30.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [6542, -1, 3207, -1, 5491, -1, 5982, -1], 'generators': [5, 340, 90], 'label': '990.16.15.a1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '15.a1.d1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.d1', 'subgroup_fusion': None, 'weyl_group': '30.1'}
  • id: 115755284
    {'ambient': '990.16', 'aut_centralizer_order': 432, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '110.1', 'aut_weyl_index': 432, 'centralizer': '55.a1.a1', 'complements': ['55.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.a1.b1', '6.a1.c1', '6.a1.d1', '9.a1.a1'], 'contains': ['90.a1.a1', '198.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7764, 8081, 5740, 5531, 1815, 7956, 2543, 4306], 'generators': [2, 90], 'label': '990.16.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.c1', '6.a1.d1', '6.a1.b1', '6.a1.a1'], 'normal_contains': ['90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
  • id: 115755285
    {'ambient': '990.16', 'aut_centralizer_order': 9, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '5280.z', 'aut_weyl_index': 9, 'centralizer': '110.a1.a1', 'complements': ['495.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.a1.c1', '6.a1.d1', '10.a1.a1', '22.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2337, 4704, 5128, 4104, 5233, 6771, 2618, 5541], 'generators': [10, 2, 90, 660], 'label': '990.16.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.c1', '6.a1.d1', '6.a1.b1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.2'}
  • id: 115755286
    {'ambient': '990.16', 'aut_centralizer_order': 90, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.29', 'aut_weyl_index': 990, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '66.a1.b1', '66.a1.c1', '66.a1.d1', '110.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [913, -1, 7122, -1, 6993, -1, 3954, -1], 'generators': [10, 2, 660], 'label': '990.16.22.a1.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.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755287
    {'ambient': '990.16', 'aut_centralizer_order': 594, 'aut_label': '30.a1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 2376, 'centralizer': '10.a1.a1', 'complements': ['33.a1.b1', '33.a1.c1', '33.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['90.a1.a1', '330.a1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5372, 6020, 1783, 3183, 5205, 5540, 2950, 5334], 'generators': [660, 90], 'label': '990.16.30.a1.a1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1'], 'normal_contains': ['90.a1.a1', '330.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '10.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 115755288
    {'ambient': '990.16', 'aut_centralizer_order': 594, 'aut_label': '30.a1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 2376, 'centralizer': '10.a1.a1', 'complements': ['33.a1.a1', '33.a1.c1', '33.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '10.a1.a1', '15.a1.b1'], 'contains': ['90.a1.a1', '330.a1.b1'], 'core': '30.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5372, 6020, 678, 2292, 5205, 5540, 3638, 7072], 'generators': [10, 90], 'label': '990.16.30.a1.b1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '30.a1.b1', 'normal_contained_in': ['6.a1.b1', '10.a1.a1'], 'normal_contains': ['90.a1.a1', '330.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.b1', 'projective_image': '990.16', 'quotient_action_image': '10.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '30.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 115755289
    {'ambient': '990.16', 'aut_centralizer_order': 594, 'aut_label': '30.a1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 2376, 'centralizer': '10.a1.a1', 'complements': ['33.a1.a1', '33.a1.d1', '33.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '10.a1.a1', '15.a1.c1'], 'contains': ['90.a1.a1', '330.a1.c1'], 'core': '30.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5372, 6020, 4158, 5420, 5205, 5540, 4669, 7941], 'generators': [670, 90], 'label': '990.16.30.a1.c1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '30.a1.c1', 'normal_contained_in': ['6.a1.c1', '10.a1.a1'], 'normal_contains': ['90.a1.a1', '330.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.c1', 'projective_image': '990.16', 'quotient_action_image': '10.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '30.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 115755290
    {'ambient': '990.16', 'aut_centralizer_order': 594, 'aut_label': '30.a1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 2376, 'centralizer': '10.a1.a1', 'complements': ['33.a1.a1', '33.a1.b1', '33.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.d1', '10.a1.a1', '15.a1.d1'], 'contains': ['90.a1.a1', '330.a1.d1'], 'core': '30.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5372, 6020, 2692, 4074, 5205, 5540, 3293, 6203], 'generators': [340, 90], 'label': '990.16.30.a1.d1', 'mobius_quo': 1, 'mobius_sub': -3, 'normal_closure': '30.a1.d1', 'normal_contained_in': ['6.a1.d1', '10.a1.a1'], 'normal_contains': ['90.a1.a1', '330.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.d1', 'projective_image': '990.16', 'quotient_action_image': '10.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '30.a1.d1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 115755291
    {'ambient': '990.16', 'aut_centralizer_order': 60, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '198.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '99.a1.a1', '165.a1.a1'], 'core': '330.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': [5195, -1, 7451, -1, 4118, -1, 7197, -1], 'generators': [5, 660, 2], 'label': '990.16.33.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755292
    {'ambient': '990.16', 'aut_centralizer_order': 60, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '198.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1', '11.a1.a1'], 'contains': ['66.a1.b1', '99.a1.a1', '165.a1.b1'], 'core': '330.a1.b1', 'coset_action_label': None, 'count': 33, 'diagramx': [5195, -1, 5776, -1, 4118, -1, 8888, -1], 'generators': [5, 10, 2], 'label': '990.16.33.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.b1', 'old_label': '33.a1.b1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755293
    {'ambient': '990.16', 'aut_centralizer_order': 60, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '198.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.c1', '11.a1.a1'], 'contains': ['66.a1.c1', '99.a1.a1', '165.a1.c1'], 'core': '330.a1.c1', 'coset_action_label': None, 'count': 33, 'diagramx': [5195, -1, 9630, -1, 4118, -1, 9416, -1], 'generators': [5, 670, 2], 'label': '990.16.33.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.c1', 'old_label': '33.a1.c1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755294
    {'ambient': '990.16', 'aut_centralizer_order': 60, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '198.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.d1', '11.a1.a1'], 'contains': ['66.a1.d1', '99.a1.a1', '165.a1.d1'], 'core': '330.a1.d1', 'coset_action_label': None, 'count': 33, 'diagramx': [5195, -1, 8736, -1, 4118, -1, 7724, -1], 'generators': [5, 340, 2], 'label': '990.16.33.a1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.d1', 'old_label': '33.a1.d1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755295
    {'ambient': '990.16', 'aut_centralizer_order': 528, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4752, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.a1.a1', '15.a1.b1', '15.a1.c1', '15.a1.d1'], 'contains': ['90.a1.a1', '495.a1.a1'], 'core': '90.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9087, -1, 3089, -1, 3584, -1, 6021, -1], 'generators': [5, 90], 'label': '990.16.45.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 115755296
    {'ambient': '990.16', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.15', 'aut_weyl_index': 72, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '15.a1.a1', '33.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5976, -1, 6110, -1, 3353, -1, 3954, -1], 'generators': [5, 660, 90, 2], 'label': '990.16.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
  • id: 115755297
    {'ambient': '990.16', 'aut_centralizer_order': 110, 'aut_label': '55.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 110, 'centralizer': '18.a1.a1', 'complements': ['18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '165.a1.a1', '165.a1.b1', '165.a1.c1', '165.a1.d1'], 'core': '55.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2185, 2314, 4404, 977, 9664, 848, 9857, 9640], 'generators': [5, 10, 660], 'label': '990.16.55.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '55.a1.a1', 'normal_contained_in': ['5.a1.a1'], 'normal_contains': ['110.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '1.1', 'quotient_action_kernel': '55.1', 'quotient_action_kernel_order': 55, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 115755298
    {'ambient': '990.16', 'aut_centralizer_order': 540, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['198.a1.a1', '330.a1.a1'], 'core': '330.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4099, -1, 7004, -1, 4394, -1, 3981, -1], 'generators': [660, 2], 'label': '990.16.66.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755299
    {'ambient': '990.16', 'aut_centralizer_order': 540, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '22.a1.a1', '33.a1.b1'], 'contains': ['198.a1.a1', '330.a1.b1'], 'core': '330.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [4099, -1, 5899, -1, 4394, -1, 5013, -1], 'generators': [10, 2], 'label': '990.16.66.a1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.a1.b1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755300
    {'ambient': '990.16', 'aut_centralizer_order': 540, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '22.a1.a1', '33.a1.c1'], 'contains': ['198.a1.a1', '330.a1.c1'], 'core': '330.a1.c1', 'coset_action_label': None, 'count': 11, 'diagramx': [4099, -1, 9111, -1, 4394, -1, 5357, -1], 'generators': [670, 2], 'label': '990.16.66.a1.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.a1.c1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755301
    {'ambient': '990.16', 'aut_centralizer_order': 540, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.d1', '22.a1.a1', '33.a1.d1'], 'contains': ['198.a1.a1', '330.a1.d1'], 'core': '330.a1.d1', 'coset_action_label': None, 'count': 11, 'diagramx': [4099, -1, 8104, -1, 4394, -1, 4325, -1], 'generators': [340, 2], 'label': '990.16.66.a1.d1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.a1.d1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755302
    {'ambient': '990.16', 'aut_centralizer_order': 4752, 'aut_label': '90.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4752, 'centralizer': '5.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.a1', '30.a1.b1', '30.a1.c1', '30.a1.d1', '45.a1.a1'], 'contains': ['990.a1.a1'], 'core': '90.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8382, 7182, 2579, 4520, 3547, 6469, 3638, 5857], 'generators': [90], 'label': '990.16.90.a1.a1', 'mobius_quo': -1, 'mobius_sub': 27, 'normal_closure': '90.a1.a1', 'normal_contained_in': ['18.a1.a1', '30.a1.c1', '30.a1.d1', '30.a1.b1', '30.a1.a1'], 'normal_contains': ['990.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '5.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 115755303
    {'ambient': '990.16', 'aut_centralizer_order': 480, 'aut_label': '99.a1', 'aut_quo_index': None, 'aut_stab_index': 99, 'aut_weyl_group': '1.1', 'aut_weyl_index': 47520, 'centralizer': '99.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '33.a1.a1', '33.a1.b1', '33.a1.c1', '33.a1.d1'], 'contains': ['198.a1.a1', '495.a1.a1'], 'core': '990.a1.a1', 'coset_action_label': None, 'count': 99, 'diagramx': [7512, -1, 7328, -1, 2773, -1, 6884, -1], 'generators': [5, 2], 'label': '990.16.99.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '99.a1.a1', 'old_label': '99.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '99.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115755304
    {'ambient': '990.16', 'aut_centralizer_order': 990, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 990, 'centralizer': '2.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['330.a1.a1', '330.a1.b1', '330.a1.c1', '330.a1.d1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1379, 4133, 3900, 2566, 7739, 3566, 5688, 8780], 'generators': [10, 660], 'label': '990.16.110.a1.a1', 'mobius_quo': 3, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1', '55.a1.a1'], 'normal_contains': ['330.a1.c1', '330.a1.d1', '330.a1.b1', '330.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '55.1', 'quotient_action_kernel_order': 55, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755305
    {'ambient': '990.16', 'aut_centralizer_order': 660, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '33.a1.a1', '55.a1.a1'], 'contains': ['330.a1.a1', '495.a1.a1'], 'core': '330.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5195, -1, 2842, -1, 5942, -1, 7197, -1], 'generators': [5, 660], 'label': '990.16.165.a1.a1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '165.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755306
    {'ambient': '990.16', 'aut_centralizer_order': 660, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '33.a1.b1', '55.a1.a1'], 'contains': ['330.a1.b1', '495.a1.a1'], 'core': '330.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5195, -1, 4383, -1, 5942, -1, 7759, -1], 'generators': [5, 10], 'label': '990.16.165.a1.b1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '165.a1.b1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755307
    {'ambient': '990.16', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.15', 'aut_weyl_index': 72, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.b1', '9.a1.a1', '15.a1.b1', '33.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5976, -1, 3340, -1, 3353, -1, 5462, -1], 'generators': [5, 10, 90, 2], 'label': '990.16.3.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '3.a1.b1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.b1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
  • id: 115755308
    {'ambient': '990.16', 'aut_centralizer_order': 660, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.c1', '33.a1.c1', '55.a1.a1'], 'contains': ['330.a1.c1', '495.a1.a1'], 'core': '330.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5195, -1, 6033, -1, 5942, -1, 8306, -1], 'generators': [5, 670], 'label': '990.16.165.a1.c1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '165.a1.c1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755309
    {'ambient': '990.16', 'aut_centralizer_order': 660, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 7920, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.d1', '33.a1.d1', '55.a1.a1'], 'contains': ['330.a1.d1', '495.a1.a1'], 'core': '330.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [5195, -1, 5663, -1, 5942, -1, 7478, -1], 'generators': [5, 340], 'label': '990.16.165.a1.d1', 'mobius_quo': None, 'mobius_sub': -11, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '165.a1.d1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 115755310
    {'ambient': '990.16', 'aut_centralizer_order': 4320, 'aut_label': '198.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '1.1', 'aut_weyl_index': 47520, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '66.a1.a1', '66.a1.b1', '66.a1.c1', '66.a1.d1', '99.a1.a1'], 'contains': ['990.a1.a1'], 'core': '990.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6668, -1, 7004, -1, 2791, -1, 4442, -1], 'generators': [2], 'label': '990.16.198.a1.a1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115755311
    {'ambient': '990.16', 'aut_centralizer_order': 5940, 'aut_label': '330.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '2.a1.a1', 'complements': ['3.a1.b1', '3.a1.c1', '3.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '66.a1.a1', '110.a1.a1', '165.a1.a1'], 'contains': ['990.a1.a1'], 'core': '330.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3142, 5800, 2667, 2829, 5205, 4611, 4724, 6647], 'generators': [660], 'label': '990.16.330.a1.a1', 'mobius_quo': -1, 'mobius_sub': 33, 'normal_closure': '330.a1.a1', 'normal_contained_in': ['30.a1.a1', '110.a1.a1'], 'normal_contains': ['990.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '330.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '165.1', 'quotient_action_kernel_order': 165, 'quotient_fusion': None, 'short_label': '330.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755312
    {'ambient': '990.16', 'aut_centralizer_order': 5940, 'aut_label': '330.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1', '3.a1.c1', '3.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['30.a1.b1', '66.a1.b1', '110.a1.a1', '165.a1.b1'], 'contains': ['990.a1.a1'], 'core': '330.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3142, 5800, 3839, 2100, 5205, 4611, 5286, 8069], 'generators': [10], 'label': '990.16.330.a1.b1', 'mobius_quo': -1, 'mobius_sub': 33, 'normal_closure': '330.a1.b1', 'normal_contained_in': ['30.a1.b1', '110.a1.a1'], 'normal_contains': ['990.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '330.a1.b1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '165.1', 'quotient_action_kernel_order': 165, 'quotient_fusion': None, 'short_label': '330.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755313
    {'ambient': '990.16', 'aut_centralizer_order': 5940, 'aut_label': '330.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1', '3.a1.d1', '3.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['30.a1.c1', '66.a1.c1', '110.a1.a1', '165.a1.c1'], 'contains': ['990.a1.a1'], 'core': '330.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3142, 5800, 5751, 4286, 5205, 4611, 5568, 8780], 'generators': [670], 'label': '990.16.330.a1.c1', 'mobius_quo': -1, 'mobius_sub': 33, 'normal_closure': '330.a1.c1', 'normal_contained_in': ['30.a1.c1', '110.a1.a1'], 'normal_contains': ['990.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '330.a1.c1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '165.1', 'quotient_action_kernel_order': 165, 'quotient_fusion': None, 'short_label': '330.a1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755314
    {'ambient': '990.16', 'aut_centralizer_order': 5940, 'aut_label': '330.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 23760, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1', '3.a1.b1', '3.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['30.a1.d1', '66.a1.d1', '110.a1.a1', '165.a1.d1'], 'contains': ['990.a1.a1'], 'core': '330.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3142, 5800, 4208, 3557, 5205, 4611, 5005, 7358], 'generators': [340], 'label': '990.16.330.a1.d1', 'mobius_quo': -1, 'mobius_sub': 33, 'normal_closure': '330.a1.d1', 'normal_contained_in': ['30.a1.d1', '110.a1.a1'], 'normal_contains': ['990.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '330.a1.d1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '165.1', 'quotient_action_kernel_order': 165, 'quotient_fusion': None, 'short_label': '330.a1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 115755315
    {'ambient': '990.16', 'aut_centralizer_order': 5280, 'aut_label': '495.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 47520, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '99.a1.a1', '165.a1.a1', '165.a1.b1', '165.a1.c1', '165.a1.d1'], 'contains': ['990.a1.a1'], 'core': '990.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7462, -1, 4491, -1, 4284, -1, 7197, -1], 'generators': [5], 'label': '990.16.495.a1.a1', 'mobius_quo': None, 'mobius_sub': 33, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '495.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '495.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115755316
    {'ambient': '990.16', 'aut_centralizer_order': None, 'aut_label': '990.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': ['90.a1.a1', '198.a1.a1', '330.a1.a1', '330.a1.b1', '330.a1.c1', '330.a1.d1', '495.a1.a1'], 'contains': [], 'core': '990.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7122, 6458, 4208, 3557, 3915, 5540, 5005, 7358], 'generators': [], 'label': '990.16.990.a1.a1', 'mobius_quo': 1, 'mobius_sub': -297, 'normal_closure': '990.a1.a1', 'normal_contained_in': ['90.a1.a1', '330.a1.c1', '330.a1.d1', '330.a1.b1', '330.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '990.a1.a1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '990.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115755317
    {'ambient': '990.16', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.15', 'aut_weyl_index': 72, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.c1', '9.a1.a1', '15.a1.c1', '33.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5976, -1, 8294, -1, 3353, -1, 6216, -1], 'generators': [5, 670, 90, 2], 'label': '990.16.3.a1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '3.a1.c1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.c1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
  • id: 115755318
    {'ambient': '990.16', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.15', 'aut_weyl_index': 72, 'centralizer': '990.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.d1', '9.a1.a1', '15.a1.d1', '33.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [5976, -1, 7102, -1, 3353, -1, 4708, -1], 'generators': [5, 340, 90, 2], 'label': '990.16.3.a1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '3.a1.d1', 'projective_image': '990.16', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.d1', 'subgroup_fusion': None, 'weyl_group': '330.2'}
  • id: 115755319
    {'ambient': '990.16', 'aut_centralizer_order': 11, 'aut_label': '5.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4320.hg', 'aut_weyl_index': 11, 'centralizer': '90.a1.a1', 'complements': ['198.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '15.a1.a1', '15.a1.b1', '15.a1.c1', '15.a1.d1', '55.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2752, 1919, 2148, 885, 8651, 2033, 6970, 8386], 'generators': [5, 10, 660, 90], 'label': '990.16.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '55.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '90.8'}
  • id: 115755320
    {'ambient': '990.16', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 216, 'centralizer': '110.a1.a1', 'complements': ['165.a1.b1', '165.a1.c1', '165.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.a1.a1', '30.a1.a1', '66.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 7007, 4532, 7151, 2598, 7956, 344, 869], 'generators': [660, 90, 2], 'label': '990.16.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.2'}
  • id: 115755321
    {'ambient': '990.16', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 216, 'centralizer': '110.a1.a1', 'complements': ['165.a1.a1', '165.a1.c1', '165.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.b1'], 'contains': ['18.a1.a1', '30.a1.b1', '66.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5838, 7007, 3340, 3224, 2598, 7956, 1860, 4701], 'generators': [10, 90, 2], 'label': '990.16.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '30.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '990.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.2'}