Abstract group data - 800.1199

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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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [4, 30, 8, 8], 'aut_gens': [[1, 2, 8, 80], [1, 2, 780, 464], [401, 530, 620, 49], [1, 482, 652, 433], [1, 723, 317, 448]], 'aut_group': None, 'aut_hash': 7210635723483188091, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 76800, 'aut_permdeg': 140, 'aut_perms': [7942222498410828028657015020916095893097783738963353230430870269598255791851922022203664272307868953142365766695116630912600960334888016003761075543653642485130949451184517781602270862447820398336489256653181441656083053811323609802168690208, 1975024803878963235691728009503483032794795180870465175304659851180117161096478684098157483576056266647517081785093830659315457288346843177961266763512646114414058223288232023822215892286730705804624322389484476389083582608893964393833416173, 12978107219321058902080422601188465159113160852556914629683358872320455062291354913530056082853157915000796590041011267793429000014222780200380450717681338026174203628186106486420118329565799792578996305550631130943973718043683076497988714886, 9781294936098949183404847853618679638390216157331414489837517890435964433465683130459966963048814196233286165321317321178086798542543526214298519514268781109482291409902100140868325003493675691700905823641009953664471802952300558894200397791], 'aut_phi_ratio': 240.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 5, 8, 1], [2, 25, 1, 1], [2, 25, 3, 1], [4, 25, 4, 2], [4, 25, 8, 1], [5, 4, 2, 1], [5, 8, 2, 1], [10, 4, 6, 1], [10, 8, 6, 1], [10, 20, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{10}^2.A_4.C_4\\wr C_2.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '96.227', 'autcent_hash': 227, 'autcent_nilpotent': False, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^2:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '800.1191', 'autcentquo_hash': 1191, 'autcentquo_nilpotent': False, 'autcentquo_order': 800, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 5, 8], [2, 25, 4], [4, 25, 16], [5, 4, 2], [5, 8, 2], [10, 4, 6], [10, 8, 6], [10, 20, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '200.42', 'commutator_count': 1, 'commutator_label': '25.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1199, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['200.42', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 5, 1, 8], [2, 25, 1, 4], [4, 25, 2, 8], [5, 4, 1, 2], [5, 8, 1, 2], [10, 4, 1, 6], [10, 8, 1, 6], [10, 20, 1, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1614480, 'exponent': 20, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '800.1199', 'hash': 1199, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [1, 4, 10, 5], 'inner_gens': [[1, 2, 8, 80], [1, 2, 376, 560], [1, 514, 8, 720], [1, 322, 168, 80]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'D_5:F_5', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [4, 16], [8, 8]], 'label': '800.1199', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D10^2.C2', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 56, 'number_divisions': 48, 'number_normal_subgroups': 155, 'number_subgroup_autclasses': 89, 'number_subgroup_classes': 526, 'number_subgroups': 4020, 'old_label': None, 'order': 800, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 143], [4, 400], [5, 24], [10, 232]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 3, 2, 2, 2, 2], 'outer_gen_pows': [124, 6, 124, 120, 0, 0, 0, 4], 'outer_gens': [[400, 403, 617, 321], [1, 2, 652, 432], [1, 2, 24, 80], [401, 402, 568, 321], [1, 2, 632, 720], [1, 2, 73, 80], [1, 3, 233, 720], [1, 402, 296, 240]], 'outer_group': '384.20163', 'outer_hash': 20163, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 12, 'outer_perms': [265929916, 213071683, 136105698, 92355916, 40723254, 766369, 1881858, 136105446], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\wr S_3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 16], [8, 8]], 'representations': {'PC': {'code': 454103470539396089848733524438044673248275890227, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -2, -2, -5, -2, -5, 36, 5274, 1641, 80, 571, 578, 11772, 7579, 3806, 124, 7853, 7860, 3947]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [106564013487, 122109387504, 36964419377, 149448494378, 89223856252, 12021289379, 98019097504]}, 'Perm': {'d': 14, 'gens': [522588249, 1037877840, 90720, 41040, 1037836816, 7743859200, 46]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}^2.C_2', 'transitive_degree': 40, '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: 140782523
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1199, 'group_order': 800, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 140782534
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1199, 'group_order': 800, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 400, 'size': 1}
  • id: 140782545
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 1199, 'group_order': 800, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1, 'size': 1}
  • id: 140782556
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 1199, 'group_order': 800, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 401, 'size': 1}
  • id: 140782567
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 5, 'group_counter': 1199, 'group_order': 800, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 40, 'size': 5}
  • id: 140782575
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 6, 'group_counter': 1199, 'group_order': 800, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 120, 'size': 5}
  • id: 140782576
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 7, 'group_counter': 1199, 'group_order': 800, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 492, 'size': 5}
  • id: 140782577
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 8, 'group_counter': 1199, 'group_order': 800, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 41, 'size': 5}
  • id: 140782578
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 9, 'group_counter': 1199, 'group_order': 800, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 121, 'size': 5}
  • id: 140782524
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 10, 'group_counter': 1199, 'group_order': 800, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 493, 'size': 5}
  • id: 140782525
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 11, 'group_counter': 1199, 'group_order': 800, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 92, 'size': 5}
  • id: 140782526
    {'aut_label': '2D', 'centralizer': '5.a1', 'counter': 12, 'group_counter': 1199, 'group_order': 800, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 93, 'size': 5}
  • id: 140782527
    {'aut_label': '2L', 'centralizer': '25.a1', 'counter': 13, 'group_counter': 1199, 'group_order': 800, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 84, 'size': 25}
  • id: 140782528
    {'aut_label': '2L', 'centralizer': '25.a1', 'counter': 14, 'group_counter': 1199, 'group_order': 800, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 5, 'size': 25}
  • id: 140782529
    {'aut_label': '2L', 'centralizer': '25.a1', 'counter': 15, 'group_counter': 1199, 'group_order': 800, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 85, 'size': 25}
  • id: 140782530
    {'aut_label': '2O', 'centralizer': '25.a1', 'counter': 16, 'group_counter': 1199, 'group_order': 800, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 4, 'size': 25}
  • id: 140782531
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 17, 'group_counter': 1199, 'group_order': 800, 'label': '4A1', 'order': 4, 'powers': [16, 17], 'representative': 2, 'size': 25}
  • id: 140782532
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 18, 'group_counter': 1199, 'group_order': 800, 'label': '4A-1', 'order': 4, 'powers': [16, 18], 'representative': 6, 'size': 25}
  • id: 140782533
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 19, 'group_counter': 1199, 'group_order': 800, 'label': '4B1', 'order': 4, 'powers': [16, 19], 'representative': 82, 'size': 25}
  • id: 140782535
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 20, 'group_counter': 1199, 'group_order': 800, 'label': '4B-1', 'order': 4, 'powers': [16, 20], 'representative': 86, 'size': 25}
  • id: 140782536
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 21, 'group_counter': 1199, 'group_order': 800, 'label': '4C1', 'order': 4, 'powers': [16, 21], 'representative': 10, 'size': 25}
  • id: 140782537
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 22, 'group_counter': 1199, 'group_order': 800, 'label': '4C-1', 'order': 4, 'powers': [16, 22], 'representative': 14, 'size': 25}
  • id: 140782538
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 23, 'group_counter': 1199, 'group_order': 800, 'label': '4D1', 'order': 4, 'powers': [16, 23], 'representative': 3, 'size': 25}
  • id: 140782539
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 24, 'group_counter': 1199, 'group_order': 800, 'label': '4D-1', 'order': 4, 'powers': [16, 24], 'representative': 7, 'size': 25}
  • id: 140782540
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 25, 'group_counter': 1199, 'group_order': 800, 'label': '4E1', 'order': 4, 'powers': [16, 25], 'representative': 90, 'size': 25}
  • id: 140782541
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 26, 'group_counter': 1199, 'group_order': 800, 'label': '4E-1', 'order': 4, 'powers': [16, 26], 'representative': 94, 'size': 25}
  • id: 140782542
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 27, 'group_counter': 1199, 'group_order': 800, 'label': '4F1', 'order': 4, 'powers': [16, 27], 'representative': 83, 'size': 25}
  • id: 140782543
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 28, 'group_counter': 1199, 'group_order': 800, 'label': '4F-1', 'order': 4, 'powers': [16, 28], 'representative': 87, 'size': 25}
  • id: 140782544
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 29, 'group_counter': 1199, 'group_order': 800, 'label': '4G1', 'order': 4, 'powers': [16, 29], 'representative': 11, 'size': 25}
  • id: 140782546
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 30, 'group_counter': 1199, 'group_order': 800, 'label': '4G-1', 'order': 4, 'powers': [16, 30], 'representative': 15, 'size': 25}
  • id: 140782547
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 31, 'group_counter': 1199, 'group_order': 800, 'label': '4H1', 'order': 4, 'powers': [16, 31], 'representative': 91, 'size': 25}
  • id: 140782548
    {'aut_label': '4C1', 'centralizer': '25.a1', 'counter': 32, 'group_counter': 1199, 'group_order': 800, 'label': '4H-1', 'order': 4, 'powers': [16, 32], 'representative': 95, 'size': 25}
  • id: 140782549
    {'aut_label': '5A', 'centralizer': '4.e1', 'counter': 33, 'group_counter': 1199, 'group_order': 800, 'label': '5A', 'order': 5, 'powers': [33, 1], 'representative': 160, 'size': 4}
  • id: 140782550
    {'aut_label': '5A', 'centralizer': '4.e1', 'counter': 34, 'group_counter': 1199, 'group_order': 800, 'label': '5B', 'order': 5, 'powers': [34, 1], 'representative': 32, 'size': 4}
  • id: 140782551
    {'aut_label': '5C', 'centralizer': '8.d1', 'counter': 35, 'group_counter': 1199, 'group_order': 800, 'label': '5C', 'order': 5, 'powers': [35, 1], 'representative': 192, 'size': 8}
  • id: 140782552
    {'aut_label': '5C', 'centralizer': '8.d1', 'counter': 36, 'group_counter': 1199, 'group_order': 800, 'label': '5D', 'order': 5, 'powers': [36, 1], 'representative': 224, 'size': 8}
  • id: 140782553
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 37, 'group_counter': 1199, 'group_order': 800, 'label': '10A', 'order': 10, 'powers': [33, 2], 'representative': 80, 'size': 4}
  • id: 140782554
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 38, 'group_counter': 1199, 'group_order': 800, 'label': '10B', 'order': 10, 'powers': [33, 3], 'representative': 161, 'size': 4}
  • id: 140782555
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 39, 'group_counter': 1199, 'group_order': 800, 'label': '10C', 'order': 10, 'powers': [33, 4], 'representative': 81, 'size': 4}
  • id: 140782557
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 40, 'group_counter': 1199, 'group_order': 800, 'label': '10D', 'order': 10, 'powers': [34, 3], 'representative': 17, 'size': 4}
  • id: 140782558
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 41, 'group_counter': 1199, 'group_order': 800, 'label': '10E', 'order': 10, 'powers': [34, 2], 'representative': 416, 'size': 4}
  • id: 140782559
    {'aut_label': '10A', 'centralizer': '4.e1', 'counter': 42, 'group_counter': 1199, 'group_order': 800, 'label': '10F', 'order': 10, 'powers': [34, 4], 'representative': 417, 'size': 4}
  • id: 140782560
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 43, 'group_counter': 1199, 'group_order': 800, 'label': '10G', 'order': 10, 'powers': [35, 2], 'representative': 96, 'size': 8}
  • id: 140782561
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 44, 'group_counter': 1199, 'group_order': 800, 'label': '10H', 'order': 10, 'powers': [36, 2], 'representative': 112, 'size': 8}
  • id: 140782562
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 45, 'group_counter': 1199, 'group_order': 800, 'label': '10I', 'order': 10, 'powers': [36, 3], 'representative': 177, 'size': 8}
  • id: 140782563
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 46, 'group_counter': 1199, 'group_order': 800, 'label': '10J', 'order': 10, 'powers': [35, 4], 'representative': 97, 'size': 8}
  • id: 140782564
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 47, 'group_counter': 1199, 'group_order': 800, 'label': '10K', 'order': 10, 'powers': [35, 3], 'representative': 337, 'size': 8}
  • id: 140782565
    {'aut_label': '10G', 'centralizer': '8.d1', 'counter': 48, 'group_counter': 1199, 'group_order': 800, 'label': '10L', 'order': 10, 'powers': [36, 4], 'representative': 113, 'size': 8}
  • id: 140782566
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 49, 'group_counter': 1199, 'group_order': 800, 'label': '10M', 'order': 10, 'powers': [34, 5], 'representative': 8, 'size': 20}
  • id: 140782568
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 50, 'group_counter': 1199, 'group_order': 800, 'label': '10N', 'order': 10, 'powers': [34, 6], 'representative': 88, 'size': 20}
  • id: 140782569
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 51, 'group_counter': 1199, 'group_order': 800, 'label': '10O', 'order': 10, 'powers': [33, 7], 'representative': 12, 'size': 20}
  • id: 140782570
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 52, 'group_counter': 1199, 'group_order': 800, 'label': '10P', 'order': 10, 'powers': [34, 8], 'representative': 9, 'size': 20}
  • id: 140782571
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 53, 'group_counter': 1199, 'group_order': 800, 'label': '10Q', 'order': 10, 'powers': [34, 9], 'representative': 89, 'size': 20}
  • id: 140782572
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 54, 'group_counter': 1199, 'group_order': 800, 'label': '10R', 'order': 10, 'powers': [33, 10], 'representative': 13, 'size': 20}
  • id: 140782573
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 55, 'group_counter': 1199, 'group_order': 800, 'label': '10S', 'order': 10, 'powers': [33, 11], 'representative': 252, 'size': 20}
  • id: 140782574
    {'aut_label': '10M', 'centralizer': '20.g1', 'counter': 56, 'group_counter': 1199, 'group_order': 800, 'label': '10T', 'order': 10, 'powers': [33, 12], 'representative': 253, 'size': 20}
• 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: 12968742
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12968753
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12968764
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12968775
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12968785
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12968786
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 12968787
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 12968788
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 12968789
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 12968743
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12968744
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12968745
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 12968746
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 12968747
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12968748
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12968749
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12968750
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1q', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 12968751
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1r', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 12968752
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1s', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 12968754
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1t', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 12968755
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1u', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, -2, 2, -2, -2, 2, 2, -2], 'schur_index': 1}
  • id: 12968756
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1v', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2], 'schur_index': 1}
  • id: 12968757
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1w', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2], 'schur_index': 1}
  • id: 12968758
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.1x', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2], 'schur_index': 1}
  • id: 12968759
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, 0, -1], 'schur_index': 1}
  • id: 12968760
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4b', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, 0, -1, 0], 'schur_index': 1}
  • id: 12968761
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4c', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, 1, -1, 1, -4, 4, -4, -1, 1, 1, -1, 1, 1, 0, -1, 1, 0, 1, 0, -1, 0], 'schur_index': 1}
  • id: 12968762
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4d', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, -4, 4, -4, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 0, 0, 1, 0, 1, 0, -1], 'schur_index': 1}
  • id: 12968763
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4e', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, -4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, -4, 4, -4, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 0, 0, -1, 0, -1, 0, 1], 'schur_index': 1}
  • id: 12968765
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4f', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, 1, -1, 1, -4, 4, -4, -1, 1, 1, -1, 1, 1, 0, 1, -1, 0, -1, 0, 1, 0], 'schur_index': 1}
  • id: 12968766
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4g', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, 1, 1, -1, 4, -4, -4, 1, 1, -1, 1, -1, 1, 0, -1, -1, 0, 1, 0, 1, 0], 'schur_index': 1}
  • id: 12968767
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4h', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, -4, -4, 4, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 0, 0, 1, 0, -1, 0, -1], 'schur_index': 1}
  • id: 12968768
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4i', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, -4, -4, 4, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 0, 0, -1, 0, 1, 0, 1], 'schur_index': 1}
  • id: 12968769
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4j', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, 1, 1, -1, 4, -4, -4, 1, 1, -1, 1, -1, 1, 0, 1, 1, 0, -1, 0, -1, 0], 'schur_index': 1}
  • id: 12968770
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4k', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, -1, 1, 1, -4, -4, 4, 1, -1, 1, 1, 1, -1, 0, 1, -1, 0, 1, 0, -1, 0], 'schur_index': 1}
  • id: 12968771
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4l', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -4, -4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, 4, -4, -4, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 1, 0, -1, 0, 1], 'schur_index': 1}
  • id: 12968772
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4m', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 4, 4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, 4, -4, -4, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 0, 0, -1, 0, 1, 0, -1], 'schur_index': 1}
  • id: 12968773
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4n', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, -1, 1, 1, -4, -4, 4, 1, -1, 1, 1, 1, -1, 0, -1, 1, 0, -1, 0, 1, 0], 'schur_index': 1}
  • id: 12968774
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4o', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, 0, 1, 1, 0, 1, 0, 1, 0], 'schur_index': 1}
  • id: 12968776
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.4p', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -4, -4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, 1, 0, 1, 0, 1], 'schur_index': 1}
  • id: 12968777
    {'cdim': 8, 'counter': 41, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8a', 'multiplicity': 1, 'nt': [10, 17], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 3, -2, -2, -2, -2, -2, -2, 3, 3, -2, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968778
    {'cdim': 8, 'counter': 42, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8b', 'multiplicity': 1, 'nt': [10, 17], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, -2, -2, -2, -2, -2, -2, -2, 3, 3, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968779
    {'cdim': 8, 'counter': 43, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8c', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 3, 2, -2, 2, 2, -2, 2, 3, -3, 2, -2, -3, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968780
    {'cdim': 8, 'counter': 44, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8d', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, 2, -2, 2, 2, -2, 2, -2, 2, -3, 3, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968781
    {'cdim': 8, 'counter': 45, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8e', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 3, 2, 2, -2, -2, 2, 2, -3, -3, -2, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968782
    {'cdim': 8, 'counter': 46, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8f', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, 2, 2, -2, -2, 2, 2, 2, 2, 3, -3, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968783
    {'cdim': 8, 'counter': 47, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8g', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 3, -2, 2, 2, 2, 2, -2, -3, 3, 2, 2, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12968784
    {'cdim': 8, 'counter': 48, 'faithful': False, 'group': '800.1199', 'group_order': 800, 'image': None, 'label': '800.1199.8h', 'multiplicity': 1, 'nt': [20, 114], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 2, 2, 2, 2, -2, 2, -2, -3, -3, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 30313617
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 800, 'label': '800.1199.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 30313628
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 30313639
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 30313650
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 30313661
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 30313669
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 30313670
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 30313671
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 30313672
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 30313618
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 30313619
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 30313620
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 30313621
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1199.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 30313622
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 400, 'label': '800.1199.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 30313623
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1199.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 30313624
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 400, 'label': '800.1199.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 30313625
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 17, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1q1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 30313626
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 18, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1q2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 30313627
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 19, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1r1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 30313629
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 20, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1r2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 30313630
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 21, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1s1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 30313631
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 22, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1s2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 30313632
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 23, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1t1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 30313633
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 24, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1t2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 30313634
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 25, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1u1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 30313635
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 26, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1u2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 30313636
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 27, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1v1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 30313637
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 28, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 200, 'label': '800.1199.1v2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 30313638
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 29, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 200, 'label': '800.1199.1w1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 30313640
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 30, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 200, 'label': '800.1199.1w2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 30313641
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 31, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 200, 'label': '800.1199.1x1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 30313642
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 32, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1', 'kernel_order': 200, 'label': '800.1199.1x2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 30313643
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1', 'kernel_order': 40, 'label': '800.1199.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 30313644
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1', 'kernel_order': 40, 'label': '800.1199.4b', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 30313645
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4c', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 30313646
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4d', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 30313647
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4e', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 30313648
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4f', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 30313649
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4g', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 30313651
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 40, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4h', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 30313652
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4i', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 30313653
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4j', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 30313654
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4k', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 30313655
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4l', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 30313656
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4m', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 30313657
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1', 'kernel_order': 20, 'label': '800.1199.4n', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 30313658
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1', 'kernel_order': 20, 'label': '800.1199.4o', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 30313659
    {'center': '20.a1', 'center_index': 20, 'center_order': 40, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1', 'kernel_order': 20, 'label': '800.1199.4p', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 30313660
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '200.42', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1', 'kernel_order': 4, 'label': '800.1199.8a', 'nt': [10, 17], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313662
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '200.42', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1', 'kernel_order': 4, 'label': '800.1199.8b', 'nt': [10, 17], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313663
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8c', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[-2, 0]], [[3, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[-3, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313664
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8d', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[3, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313665
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8e', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[-2, 0]], [[3, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313666
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8f', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[-3, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313667
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8g', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30313668
    {'center': '200.a1', 'center_index': 200, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1199', 'group_counter': 1199, 'group_order': 800, 'image': None, 'image_isoclass': '400.210', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1199.8h', 'nt': [20, 114], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 110936629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 800, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '800.1199.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1199', 'subgroup_hash': 1199, 'subgroup_order': 800, 'subgroup_tex': 'D_{10}^2.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110936640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 400, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '800.1199.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.210', 'subgroup_hash': 210, 'subgroup_order': 400, 'subgroup_tex': 'D_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.218', 'subgroup_hash': 218, 'subgroup_order': 400, 'subgroup_tex': 'D_{10}^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.216', 'subgroup_hash': 216, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.217', 'subgroup_hash': 217, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.47', 'subgroup_hash': 47, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.48', 'subgroup_hash': 48, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 200, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.50', 'subgroup_hash': 50, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 200, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.51', 'subgroup_hash': 51, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 12, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '800.1199.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.5.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.236', 'subgroup_hash': 236, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 100, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 100, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.10.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.10.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.51', 'subgroup_hash': 51, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.10.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.10.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.10.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 50, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 50, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 50, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 50, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 40, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.20.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.20.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '800.1199.25.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 110936665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 25, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '800.1199.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 110936666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.40.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 20, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.40.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936677
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936678
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936679
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.40.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.50.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.50.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 110936682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.50.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.50.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936685
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 10, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '800.1199.80.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 110936686
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1199.80.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936687
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.80.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': 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: 110936688
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.80.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': 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: 110936689
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.80.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936690
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.80.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936691
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.80.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936692
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.80.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110936694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110936696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110936699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 110936700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.100.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936701
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 5, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '800.1199.160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '160.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '160.236', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 236, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times F_5', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 110936702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.160.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, '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': 0}
  • id: 110936703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': True, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '800.1199.200.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5:F_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.200.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.200.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.200.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.200.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1199.200.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110936710
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.200.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.200.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110936712
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': True, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '800.1199.400.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '400.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.210', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}:F_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110936713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.400.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110936714
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.400.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110936715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1199.400.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110936716
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1199', 'ambient_counter': 1199, 'ambient_order': 800, 'ambient_tex': 'D_{10}^2.C_2', 'central': True, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 1, 'counter': 89, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '800.1199.800.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '800.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '800.1199', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1199, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}^2.C_2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C7'], '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: 110936671
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '20.c1', '20.h1'], 'contains': ['80.a1', '80.e1', '200.d1'], 'core': '80.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4226, -1, 7345, -1], 'generators': [1, 16, 724], 'label': '800.1199.40.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.f1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936629
    {'ambient': '800.1199', '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': '200.a1', 'complements': ['800.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '5.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6851, 5286, 3875, 5605], 'generators': [1, 656, 40, 400, 2, 160, 4], 'label': '800.1199.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936630
    {'ambient': '800.1199', 'aut_centralizer_order': 20, 'aut_label': '4.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1920.239985', 'aut_weyl_index': 40, 'centralizer': '40.b1', 'complements': ['200.g1', '200.h1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.d1', '20.a1', '20.g1'], 'core': '4.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [2118, 891, 8197, 1151], 'generators': [1, 400, 656, 40, 160], 'label': '800.1199.4.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.a1', '8.d1', '20.a1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110936631
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4800.bn', 'aut_weyl_index': 16, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.b1', '8.c1', '8.d1', '20.h1', '20.i1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [4850, 3891, 5754, 4253], 'generators': [1, 400, 656, 4, 160], 'label': '800.1199.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.b1', '8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936632
    {'ambient': '800.1199', 'aut_centralizer_order': 6, 'aut_label': '4.g1', 'aut_quo_index': 1, 'aut_stab_index': 16, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': ['200.a1', '200.b1', '200.d1', '200.e1'], 'conjugacy_class_count': 16, 'contained_in': ['2.a1'], 'contains': ['8.f1', '8.g1', '8.h1', '20.j1'], 'core': '4.g1', 'coset_action_label': None, 'count': 16, 'diagramx': [7750, 9149, 939, 9691], 'generators': [2, 4, 656, 760, 160], 'label': '800.1199.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.f1', '8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '800.1199', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936633
    {'ambient': '800.1199', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1920.240397', 'aut_weyl_index': 40, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['10.a1', '10.b1', '10.c1', '10.e1', '25.a1'], 'core': '20.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8409, -1, 4443, -1], 'generators': [1, 16, 520, 400, 2, 4], 'label': '800.1199.5.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '5.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936634
    {'ambient': '800.1199', 'aut_centralizer_order': 40, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 12, 'aut_weyl_group': '160.203', 'aut_weyl_index': 480, 'centralizer': '40.b1', 'complements': ['100.c1', '100.g1', '100.d1'], 'conjugacy_class_count': 12, 'contained_in': ['4.a1', '4.b1', '4.e1'], 'contains': ['16.a1', '16.b1', '40.a1', '40.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3397, 2528, 7745, 2844], 'generators': [40, 656, 160, 400], 'label': '800.1199.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.e1'], 'normal_contains': ['16.a1', '16.b1', '40.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '400.210', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110936635
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 42, 'aut_stab_index': 3, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '4.c1', '4.d1', '4.f1'], 'contains': ['16.a1', '16.c1', '16.d1', '40.d1', '40.e1'], 'core': '8.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5324, 5884, 4532, 6314], 'generators': [4, 656, 160, 400], 'label': '800.1199.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.c1', '4.d1', '4.f1'], 'normal_contains': ['16.a1', '16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936636
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 48, 'centralizer': '200.a1', 'complements': ['100.g1'], 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '4.f1'], 'contains': ['16.a1', '16.c1', '40.f1', '40.g1'], 'core': '8.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [2776, 3867, 6404, 4228], 'generators': [1, 656, 160, 724], 'label': '800.1199.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.f1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '400.210', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936637
    {'ambient': '800.1199', 'aut_centralizer_order': 400, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '192.379', 'aut_weyl_index': 400, 'centralizer': '8.d1', 'complements': ['100.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.f1'], 'contains': ['16.a1', '40.b1', '40.h1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1106, 1423, 8197, 1701], 'generators': [1, 656, 160, 400], 'label': '800.1199.8.d1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': ['4.e1', '4.f1'], 'normal_contains': ['16.a1', '40.b1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '200.42', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 110936638
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': ['100.c1', '100.g1', '100.d1'], 'conjugacy_class_count': 12, 'contained_in': ['4.a1', '4.b1'], 'contains': ['16.b1', '16.c1', '40.i1'], 'core': '8.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [3951, 4875, 5991, 5271], 'generators': [724, 656, 160, 40], 'label': '800.1199.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.b1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '800.1199', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936639
    {'ambient': '800.1199', 'aut_centralizer_order': 24, 'aut_label': '8.f1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.g1'], 'contains': ['16.b1', '16.d1', '40.j1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [5944, 6891, 4119, 7356], 'generators': [4, 656, 160, 760], 'label': '800.1199.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.a1', '4.g1'], 'normal_contains': ['16.b1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936640
    {'ambient': '800.1199', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '3200.ih', 'aut_weyl_index': 24, 'centralizer': '200.a1', 'complements': ['400.a1', '400.b1', '400.c1'], 'conjugacy_class_count': 12, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '4.g1', '10.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7506, 7513, 2491, 7998], 'generators': [2, 160, 400, 4, 40, 656], 'label': '800.1199.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '400.210', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936641
    {'ambient': '800.1199', 'aut_centralizer_order': 24, 'aut_label': '8.g1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': ['100.e1', '100.b1'], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.g1'], 'contains': ['16.d1', '40.k1', '40.l1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7569, 7681, 157, 8932], 'generators': [2, 656, 160, 4], 'label': '800.1199.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.c1', '4.g1'], 'normal_contains': ['16.d1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '800.1199', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936642
    {'ambient': '800.1199', 'aut_centralizer_order': 24, 'aut_label': '8.h1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': ['100.e1', '100.b1'], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.g1'], 'contains': ['16.d1', '40.m1'], 'core': '8.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [6970, 8505, 939, 8081], 'generators': [10, 496, 160, 548], 'label': '800.1199.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.d1', '4.g1'], 'normal_contains': ['16.d1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '800.1199', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936643
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '80.50', 'aut_weyl_index': 960, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['2.a1', '5.a1'], 'contains': ['20.b1', '20.d1', '20.f1', '20.j1', '50.a1'], 'core': '40.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9385, -1, 2597, -1], 'generators': [2, 400, 4, 520, 16], 'label': '800.1199.10.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '10.a1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936644
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 160, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '5.a1'], 'contains': ['20.a1', '20.b1', '20.c1', '20.g1', '20.h1', '50.b1'], 'core': '20.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5164, -1, 7141, -1], 'generators': [1, 40, 400, 372, 16], 'label': '800.1199.10.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '10.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936645
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 160, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '5.a1'], 'contains': ['20.d1', '20.h1', '50.c1'], 'core': '40.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [8577, -1, 3627, -1], 'generators': [1, 400, 4, 2, 16], 'label': '800.1199.10.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '10.c1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936646
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 160, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['20.e1', '20.i1', '50.c1'], 'core': '200.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6830, -1, 3112, -1], 'generators': [1, 400, 4, 2, 656], 'label': '800.1199.10.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '10.d1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936647
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 160, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '5.a1'], 'contains': ['20.f1', '20.h1', '50.d1'], 'core': '40.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [7900, -1, 4142, -1], 'generators': [1, 400, 548, 10, 16], 'label': '800.1199.10.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '10.e1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936648
    {'ambient': '800.1199', 'aut_centralizer_order': 800, 'aut_label': '16.a1', 'aut_quo_index': 24, 'aut_stab_index': 3, 'aut_weyl_group': '32.11', 'aut_weyl_index': 2400, 'centralizer': '8.d1', 'complements': ['50.a1'], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '80.a1', '80.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1106, 3319, 6391, 3803], 'generators': [400, 160, 656], 'label': '800.1199.16.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '80.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '400.210', 'quotient_action_image': '8.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 110936649
    {'ambient': '800.1199', 'aut_centralizer_order': 120, 'aut_label': '16.b1', 'aut_quo_index': 8, 'aut_stab_index': 8, 'aut_weyl_group': '80.30', 'aut_weyl_index': 960, 'centralizer': '40.b1', 'complements': ['50.c1', '50.a1', '50.d1'], 'conjugacy_class_count': 8, 'contained_in': ['8.a1', '8.e1', '8.f1'], 'contains': ['32.a1', '80.b1', '80.d1'], 'core': '16.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3662, 4529, 5896, 5054], 'generators': [760, 160, 656], 'label': '800.1199.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.e1', '8.f1'], 'normal_contains': ['32.a1', '80.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '800.1199', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 110936650
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '16.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': ['50.a1'], 'conjugacy_class_count': 3, 'contained_in': ['8.b1', '8.c1', '8.e1'], 'contains': ['32.a1', '80.e1', '80.f1'], 'core': '16.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3128, 5456, 4948, 6013], 'generators': [724, 160, 656], 'label': '800.1199.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.c1', '8.e1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '800.1199', 'quotient_action_image': '8.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936651
    {'ambient': '800.1199', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '19200.x', 'aut_weyl_index': 4, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.e1', '4.f1', '10.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4655, 3198, 6077, 3536], 'generators': [1, 160, 40, 400, 4, 656], 'label': '800.1199.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936652
    {'ambient': '800.1199', 'aut_centralizer_order': 96, 'aut_label': '16.d1', 'aut_quo_index': 210, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 96, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.f1', '8.g1', '8.h1'], 'contains': ['32.a1', '80.g1', '80.h1'], 'core': '16.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5948, 6891, 3489, 7356], 'generators': [4, 160, 656], 'label': '800.1199.16.d1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.d1', 'normal_contained_in': ['8.b1', '8.f1', '8.g1', '8.h1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936653
    {'ambient': '800.1199', 'aut_centralizer_order': 80, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 160, 'centralizer': '20.a1', 'complements': ['40.k1', '40.l1', '40.m1'], 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '10.b1'], 'contains': ['40.a1', '40.b1', '100.e1'], 'core': '20.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1521, 851, 9161, 584], 'generators': [1, 400, 160, 520], 'label': '800.1199.20.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['40.a1', '40.b1'], 'normalizer': '1.a1', 'old_label': '20.a1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936654
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.a1', '10.a1', '10.b1'], 'contains': ['40.a1', '40.c1', '40.d1', '40.i1', '40.j1', '100.a1'], 'core': '40.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5210, -1, 6942, -1], 'generators': [372, 400, 16, 40], 'label': '800.1199.20.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.b1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936655
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '80.50', 'aut_weyl_index': 960, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.b1', '10.b1'], 'contains': ['40.a1', '40.c1', '40.f1', '40.i1', '100.b1'], 'core': '40.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4324, -1, 8640, -1], 'generators': [1, 40, 16, 724], 'label': '800.1199.20.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.c1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936656
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.c1', '10.a1', '10.c1'], 'contains': ['40.d1', '40.k1', '100.c1'], 'core': '80.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [9277, -1, 1758, -1], 'generators': [2, 4, 16, 400], 'label': '800.1199.20.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.d1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936657
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.c1', '10.d1'], 'contains': ['40.e1', '40.l1', '100.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7140, -1, 1313, -1], 'generators': [2, 4, 656, 400], 'label': '800.1199.20.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '20.e1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936658
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.d1', '10.a1', '10.e1'], 'contains': ['40.d1', '40.m1', '100.d1'], 'core': '80.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8807, -1, 2204, -1], 'generators': [10, 548, 16, 400], 'label': '800.1199.20.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.f1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936659
    {'ambient': '800.1199', 'aut_centralizer_order': 80, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.186', 'aut_weyl_index': 800, 'centralizer': '20.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '10.b1'], 'contains': ['40.b1', '40.c1', '100.e1'], 'core': '40.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2118, -1, 9726, -1], 'generators': [1, 400, 16, 40], 'label': '800.1199.20.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.g1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936660
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '120.36', 'aut_weyl_index': 640, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.f1', '10.b1', '10.c1', '10.e1'], 'contains': ['40.b1', '40.d1', '40.f1', '100.f1'], 'core': '40.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [6362, -1, 5592, -1], 'generators': [1, 400, 16, 4], 'label': '800.1199.20.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.h1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936661
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '20.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '120.36', 'aut_weyl_index': 640, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.f1', '10.d1'], 'contains': ['40.e1', '40.g1', '40.h1', '100.f1'], 'core': '200.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3641, -1, 5070, -1], 'generators': [1, 400, 656, 4], 'label': '800.1199.20.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '20.i1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936662
    {'ambient': '800.1199', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '19200.x', 'aut_weyl_index': 4, 'centralizer': '200.a1', 'complements': ['400.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.f1', '10.c1', '10.d1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6851, 4488, 3221, 6430], 'generators': [1, 160, 400, 4, 2, 656], 'label': '800.1199.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '200.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936663
    {'ambient': '800.1199', 'aut_centralizer_order': 24, 'aut_label': '20.j1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['4.g1', '10.a1'], 'contains': ['40.j1', '40.k1', '40.m1', '100.g1'], 'core': '80.b1', 'coset_action_label': None, 'count': 160, 'diagramx': [9747, -1, 566, -1], 'generators': [2, 4, 16, 120], 'label': '800.1199.20.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '20.j1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936664
    {'ambient': '800.1199', 'aut_centralizer_order': 16, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '192.1538', 'aut_weyl_index': 400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1'], 'contains': ['50.a1', '50.b1', '50.c1', '50.d1'], 'core': '200.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8144, -1, 4661, -1], 'generators': [1, 2, 520, 400], 'label': '800.1199.25.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '25.a1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936665
    {'ambient': '800.1199', 'aut_centralizer_order': 2400, 'aut_label': '32.a1', 'aut_quo_index': 112, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 2400, 'centralizer': '8.d1', 'complements': ['25.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'contains': ['160.a1', '160.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [838, 4529, 5087, 5054], 'generators': [656, 160], 'label': '800.1199.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'normal_contains': ['160.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '800.1199', 'quotient_action_image': '8.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 110936666
    {'ambient': '800.1199', 'aut_centralizer_order': 160, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '20.a1', 'complements': ['20.d1', '20.e1', '20.j1', '20.f1'], 'conjugacy_class_count': 12, 'contained_in': ['8.a1', '20.a1', '20.b1', '20.c1'], 'contains': ['80.a1', '80.b1', '200.b1'], 'core': '40.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2756, 2658, 8207, 2752], 'generators': [520, 160, 400], 'label': '800.1199.40.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1', 'normal_contained_in': ['8.a1', '20.a1'], 'normal_contains': ['80.a1', '80.b1'], 'normalizer': '1.a1', 'old_label': '40.a1', 'projective_image': '400.210', 'quotient_action_image': '4.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936667
    {'ambient': '800.1199', 'aut_centralizer_order': 1600, 'aut_label': '40.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.5', 'aut_weyl_index': 3200, 'centralizer': '4.e1', 'complements': ['20.j1'], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '20.a1', '20.g1', '20.h1'], 'contains': ['80.a1', '200.a1'], 'core': '40.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1646, 1641, 9161, 1701], 'generators': [1, 16, 400], 'label': '800.1199.40.b1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '40.b1', 'normal_contained_in': ['8.d1', '20.a1'], 'normal_contains': ['80.a1', '200.a1'], 'normalizer': '1.a1', 'old_label': '40.b1', 'projective_image': '200.42', 'quotient_action_image': '4.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936668
    {'ambient': '800.1199', 'aut_centralizer_order': 160, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.2', 'aut_weyl_index': 9600, 'centralizer': '20.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.a1', '20.b1', '20.c1', '20.g1'], 'contains': ['80.a1', '80.d1', '200.b1'], 'core': '80.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3194, -1, 8623, -1], 'generators': [40, 16, 400], 'label': '800.1199.40.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.c1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936669
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '20.b1', '20.d1', '20.f1', '20.h1'], 'contains': ['80.a1', '80.e1', '80.g1', '200.c1'], 'core': '80.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6743, -1, 4377, -1], 'generators': [4, 16, 400], 'label': '800.1199.40.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.d1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936670
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '20.e1', '20.i1'], 'contains': ['80.c1', '80.f1', '80.h1', '200.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3916, -1, 3789, -1], 'generators': [4, 656, 400], 'label': '800.1199.40.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '40.e1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936672
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '40.12', 'aut_weyl_index': 1920, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '20.i1'], 'contains': ['80.c1', '80.f1', '200.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2445, -1, 5248, -1], 'generators': [1, 656, 724], 'label': '800.1199.40.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '40.g1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936673
    {'ambient': '800.1199', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '19200.x', 'aut_weyl_index': 4, 'centralizer': '200.a1', 'complements': ['400.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.f1', '10.e1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6160, 6085, 3875, 4779], 'generators': [1, 160, 400, 548, 10, 496], 'label': '800.1199.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '200.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936674
    {'ambient': '800.1199', 'aut_centralizer_order': 800, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 3200, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '20.i1'], 'contains': ['80.c1', '200.a1'], 'core': '200.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [253, -1, 6929, -1], 'generators': [1, 656, 400], 'label': '800.1199.40.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '40.h1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936675
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.e1', '20.b1', '20.c1'], 'contains': ['80.b1', '80.d1', '80.e1', '200.e1'], 'core': '80.b1', 'coset_action_label': None, 'count': 120, 'diagramx': [4665, -1, 7639, -1], 'generators': [724, 16, 40], 'label': '800.1199.40.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.i1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936676
    {'ambient': '800.1199', 'aut_centralizer_order': 96, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.f1', '20.b1', '20.j1'], 'contains': ['80.b1', '80.d1', '80.g1', '200.f1'], 'core': '80.b1', 'coset_action_label': None, 'count': 40, 'diagramx': [6122, -1, 4083, -1], 'generators': [660, 16, 760], 'label': '800.1199.40.j1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.j1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936677
    {'ambient': '800.1199', 'aut_centralizer_order': 96, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.g1', '20.d1', '20.j1'], 'contains': ['80.g1', '200.g1'], 'core': '160.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9667, -1, 1633, -1], 'generators': [2, 16, 4], 'label': '800.1199.40.k1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.k1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936678
    {'ambient': '800.1199', 'aut_centralizer_order': 48, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.g1', '20.e1'], 'contains': ['80.h1', '200.g1'], 'core': '800.a1', 'coset_action_label': '40T865', 'count': 80, 'diagramx': [7297, -1, 1355, -1], 'generators': [2, 656, 4], 'label': '800.1199.40.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '40.l1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936679
    {'ambient': '800.1199', 'aut_centralizer_order': 96, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.h1', '20.f1', '20.j1'], 'contains': ['80.g1', '200.h1'], 'core': '160.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8883, -1, 1871, -1], 'generators': [10, 16, 548], 'label': '800.1199.40.m1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '40.m1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936680
    {'ambient': '800.1199', 'aut_centralizer_order': 32, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '8.5', 'aut_weyl_index': 9600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['10.a1', '25.a1'], 'contains': ['100.a1', '100.c1', '100.d1', '100.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [8981, -1, 2686, -1], 'generators': [2, 520, 400], 'label': '800.1199.50.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.a1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936681
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '48.48', 'aut_weyl_index': 1600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1', '25.a1'], 'contains': ['100.a1', '100.b1', '100.e1', '100.f1'], 'core': '200.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6272, -1, 7339, -1], 'generators': [1, 4, 520, 400], 'label': '800.1199.50.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.b1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936682
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '24.12', 'aut_weyl_index': 3200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1', '10.d1', '25.a1'], 'contains': ['100.c1', '100.f1'], 'core': '200.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8032, -1, 3205, -1], 'generators': [1, 2, 400], 'label': '800.1199.50.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.c1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936683
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '50.d1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '48.48', 'aut_weyl_index': 1600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1', '25.a1'], 'contains': ['100.d1', '100.f1'], 'core': '200.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7486, -1, 3723, -1], 'generators': [1, 10, 400], 'label': '800.1199.50.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.d1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936684
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 48, 'centralizer': '200.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.e1', '8.f1', '20.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5453, 5286, 5183, 5696], 'generators': [4, 400, 656, 40, 160], 'label': '800.1199.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.e1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936685
    {'ambient': '800.1199', 'aut_centralizer_order': 3200, 'aut_label': '80.a1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 19200, 'centralizer': '4.e1', 'complements': ['10.a1'], 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '40.a1', '40.b1', '40.c1', '40.d1', '40.f1'], 'contains': ['160.a1', '400.a1'], 'core': '80.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2950, 2658, 6966, 2752], 'generators': [400, 16], 'label': '800.1199.80.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '80.a1', 'normal_contained_in': ['16.a1', '40.a1', '40.b1'], 'normal_contains': ['160.a1', '400.a1'], 'normalizer': '1.a1', 'old_label': '80.a1', 'projective_image': '400.210', 'quotient_action_image': '4.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936686
    {'ambient': '800.1199', 'aut_centralizer_order': 480, 'aut_label': '80.b1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '20.a1', 'complements': ['10.c1', '10.d1', '10.a1', '10.e1'], 'conjugacy_class_count': 8, 'contained_in': ['16.b1', '40.a1', '40.i1', '40.j1'], 'contains': ['160.a1', '400.b1'], 'core': '80.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3571, 3302, 6140, 3419], 'generators': [440, 160], 'label': '800.1199.80.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.b1', 'normal_contained_in': ['16.b1', '40.a1'], 'normal_contains': ['160.a1'], 'normalizer': '1.a1', 'old_label': '80.b1', 'projective_image': '800.1199', 'quotient_action_image': '4.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936687
    {'ambient': '800.1199', 'aut_centralizer_order': 1600, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 19200, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '40.e1', '40.g1', '40.h1'], 'contains': ['160.b1', '400.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1117, -1, 5367, -1], 'generators': [400, 656], 'label': '800.1199.80.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '80.c1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936688
    {'ambient': '800.1199', 'aut_centralizer_order': 480, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.1', 'aut_weyl_index': 19200, 'centralizer': '20.g1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.b1', '40.c1', '40.i1', '40.j1'], 'contains': ['160.a1', '400.b1'], 'core': '160.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3909, -1, 6675, -1], 'generators': [760, 16], 'label': '800.1199.80.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '80.d1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936689
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.c1', '40.d1', '40.f1', '40.i1'], 'contains': ['160.a1', '400.c1'], 'core': '160.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4585, -1, 5632, -1], 'generators': [724, 16], 'label': '800.1199.80.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '80.e1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936690
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.c1', '40.e1', '40.g1'], 'contains': ['160.b1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2162, -1, 4832, -1], 'generators': [724, 656], 'label': '800.1199.80.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '80.f1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936691
    {'ambient': '800.1199', 'aut_centralizer_order': 384, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '40.d1', '40.j1', '40.k1', '40.m1'], 'contains': ['160.a1', '400.d1'], 'core': '160.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7011, -1, 3842, -1], 'generators': [4, 16], 'label': '800.1199.80.g1', 'mobius_quo': None, 'mobius_sub': -64, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '80.g1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936692
    {'ambient': '800.1199', 'aut_centralizer_order': 192, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 3840, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '40.e1', '40.l1'], 'contains': ['160.b1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5077, -1, 3604, -1], 'generators': [4, 656], 'label': '800.1199.80.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.d1', 'old_label': '80.h1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 110936714
    {'ambient': '800.1199', 'aut_centralizer_order': 1024, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['80.e1', '80.f1', '200.c1', '200.d1', '200.e1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4359, -1, 5632, -1], 'generators': [724], 'label': '800.1199.400.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.c1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936693
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['20.b1', '50.a1', '50.b1'], 'contains': ['200.b1', '200.c1', '200.e1', '200.f1'], 'core': '400.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6349, -1, 5533, -1], 'generators': [4, 520, 400], 'label': '800.1199.100.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.a1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936694
    {'ambient': '800.1199', 'aut_centralizer_order': 64, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '8.3', 'aut_weyl_index': 9600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['20.c1', '50.b1'], 'contains': ['200.b1', '200.d1', '200.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4885, -1, 7923, -1], 'generators': [1, 724, 40], 'label': '800.1199.100.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.b1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936695
    {'ambient': '800.1199', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '3200.w', 'aut_weyl_index': 24, 'centralizer': '200.a1', 'complements': ['200.g1', '200.h1'], 'conjugacy_class_count': 6, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.c1', '8.e1', '20.c1'], 'core': '4.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3951, 2496, 6404, 2811], 'generators': [1, 40, 656, 724, 160], 'label': '800.1199.4.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.a1', '8.c1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '400.210', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936696
    {'ambient': '800.1199', 'aut_centralizer_order': 256, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['20.d1', '20.e1', '50.a1', '50.c1'], 'contains': ['200.c1', '200.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [8943, -1, 2663, -1], 'generators': [2, 400], 'label': '800.1199.100.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.c1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936697
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '4.2', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['20.f1', '50.a1', '50.d1'], 'contains': ['200.c1', '200.h1'], 'core': '400.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [8468, -1, 3112, -1], 'generators': [10, 400], 'label': '800.1199.100.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.d1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936698
    {'ambient': '800.1199', 'aut_centralizer_order': 320, 'aut_label': '100.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 3200, 'centralizer': '5.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.a1', '20.g1', '50.b1'], 'contains': ['200.a1', '200.b1'], 'core': '200.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2145, -1, 9568, -1], 'generators': [1, 520, 400], 'label': '800.1199.100.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '100.e1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936699
    {'ambient': '800.1199', 'aut_centralizer_order': 512, 'aut_label': '100.f1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '6.1', 'aut_weyl_index': 12800, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.h1', '20.i1', '50.b1', '50.c1', '50.d1'], 'contains': ['200.a1', '200.c1', '200.d1'], 'core': '200.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6064, -1, 4661, -1], 'generators': [1, 4, 400], 'label': '800.1199.100.f1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.f1', 'projective_image': '200.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936700
    {'ambient': '800.1199', 'aut_centralizer_order': 96, 'aut_label': '100.g1', 'aut_quo_index': None, 'aut_stab_index': 400, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['20.j1', '50.a1'], 'contains': ['200.f1', '200.g1', '200.h1'], 'core': '800.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [9549, -1, 2214, -1], 'generators': [2, 120], 'label': '800.1199.100.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.g1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936701
    {'ambient': '800.1199', 'aut_centralizer_order': 9600, 'aut_label': '160.a1', 'aut_quo_index': 14, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 19200, 'centralizer': '4.e1', 'complements': ['5.a1'], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '80.a1', '80.b1', '80.d1', '80.e1', '80.g1'], 'contains': ['800.a1'], 'core': '160.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3547, 3206, 5869, 3386], 'generators': [16], 'label': '800.1199.160.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '160.a1', 'normal_contained_in': ['32.a1', '80.a1', '80.b1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '160.a1', 'projective_image': '800.1199', 'quotient_action_image': '4.1', 'quotient_action_kernel': '40.14', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '160.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936702
    {'ambient': '800.1199', 'aut_centralizer_order': 4800, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 19200, 'centralizer': '8.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '80.c1', '80.f1', '80.h1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1518, -1, 5087, -1], 'generators': [656], 'label': '800.1199.160.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '160.b1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 110936703
    {'ambient': '800.1199', 'aut_centralizer_order': 12800, 'aut_label': '200.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 12800, 'centralizer': '1.a1', 'complements': ['4.g1'], 'conjugacy_class_count': 1, 'contained_in': ['40.b1', '40.h1', '100.e1', '100.f1'], 'contains': ['400.a1'], 'core': '200.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1727, 2165, 7246, 1877], 'generators': [1, 400], 'label': '800.1199.200.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '200.a1', 'normal_contained_in': ['40.b1'], 'normal_contains': ['400.a1'], 'normalizer': '1.a1', 'old_label': '200.a1', 'projective_image': '200.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.42', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936704
    {'ambient': '800.1199', 'aut_centralizer_order': 640, 'aut_label': '200.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '5.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['40.a1', '40.c1', '100.a1', '100.b1', '100.e1'], 'contains': ['400.a1', '400.b1'], 'core': '400.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [3281, -1, 7923, -1], 'generators': [520, 400], 'label': '800.1199.200.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '200.b1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936705
    {'ambient': '800.1199', 'aut_centralizer_order': 1024, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['40.d1', '40.e1', '100.a1', '100.c1', '100.d1', '100.f1'], 'contains': ['400.a1', '400.c1', '400.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6217, -1, 4377, -1], 'generators': [4, 400], 'label': '800.1199.200.c1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.c1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936706
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 48, 'centralizer': '200.a1', 'complements': ['200.b1', '200.e1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.g1', '20.d1', '20.e1'], 'core': '4.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7262, 6682, 1481, 8523], 'generators': [2, 4, 656, 400, 160], 'label': '800.1199.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '400.210', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 110936707
    {'ambient': '800.1199', 'aut_centralizer_order': 512, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['40.f1', '40.g1', '100.b1', '100.f1'], 'contains': ['400.a1', '400.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4241, -1, 5886, -1], 'generators': [1, 724], 'label': '800.1199.200.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.d1', 'projective_image': '400.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936708
    {'ambient': '800.1199', 'aut_centralizer_order': 128, 'aut_label': '200.e1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['40.i1', '100.a1', '100.b1'], 'contains': ['400.b1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4885, -1, 6394, -1], 'generators': [724, 40], 'label': '800.1199.200.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.e1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936709
    {'ambient': '800.1199', 'aut_centralizer_order': 384, 'aut_label': '200.f1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.j1', '100.a1', '100.g1'], 'contains': ['400.b1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6558, -1, 4096, -1], 'generators': [324, 440], 'label': '800.1199.200.f1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.f1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936710
    {'ambient': '800.1199', 'aut_centralizer_order': 768, 'aut_label': '200.g1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.k1', '40.l1', '100.c1', '100.g1'], 'contains': ['400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [9702, -1, 2214, -1], 'generators': [2], 'label': '800.1199.200.g1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.g1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936711
    {'ambient': '800.1199', 'aut_centralizer_order': 384, 'aut_label': '200.h1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 38400, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.m1', '100.d1', '100.g1'], 'contains': ['400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [8820, -1, 2782, -1], 'generators': [10], 'label': '800.1199.200.h1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.h1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936712
    {'ambient': '800.1199', 'aut_centralizer_order': 25600, 'aut_label': '400.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '1.a1', 'complements': ['2.a1'], 'conjugacy_class_count': 3, 'contained_in': ['80.a1', '80.c1', '200.a1', '200.b1', '200.c1', '200.d1'], 'contains': ['800.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3281, 2658, 6378, 2752], 'generators': [400], 'label': '800.1199.400.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '400.a1', 'normal_contained_in': ['80.a1', '200.a1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '400.a1', 'projective_image': '400.210', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.210', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936713
    {'ambient': '800.1199', 'aut_centralizer_order': 1920, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '5.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['80.b1', '80.d1', '200.b1', '200.e1', '200.f1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3878, -1, 6140, -1], 'generators': [440], 'label': '800.1199.400.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1', 'old_label': '400.b1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936715
    {'ambient': '800.1199', 'aut_centralizer_order': 3072, 'aut_label': '400.d1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 76800, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.g1', '80.h1', '200.c1', '200.f1', '200.g1', '200.h1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6558, -1, 3842, -1], 'generators': [4], 'label': '800.1199.400.d1', 'mobius_quo': None, 'mobius_sub': 64, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.d1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936716
    {'ambient': '800.1199', 'aut_centralizer_order': None, 'aut_label': '800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['160.a1', '160.b1', '400.a1', '400.b1', '400.c1', '400.d1'], 'contains': [], 'core': '800.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3651, 2908, 5751, 3052], 'generators': [], 'label': '800.1199.800.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '800.a1', 'normal_contained_in': ['160.a1', '400.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '800.a1', 'projective_image': '800.1199', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110936717
    {'ambient': '800.1199', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 48, 'centralizer': '200.a1', 'complements': ['200.b1', '200.e1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.h1', '20.f1'], 'core': '4.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [6645, 8109, 2065, 7047], 'generators': [10, 548, 496, 400, 160], 'label': '800.1199.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '400.210', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}