Abstract group data - 800.1194

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [4, 6, 4, 4, 10, 10], 'aut_gens': [[1563129, 1047513, 891283, 547511, 625626, 1172503, 1565004], [1719399, 1299382, 549469, 547516, 469376, 1406883, 1565004], [1641269, 1016283, 563134, 547506, 547516, 861892, 1565004], [1563144, 1049393, 1127543, 469386, 703761, 1172513, 1565004], [1797524, 1127503, 1125673, 703771, 625646, 1328758, 1565004], [1641259, 1299397, 1455742, 547511, 625626, 1485023, 1565004], [1641269, 1455632, 813153, 547511, 625626, 1485013, 1565004]], 'aut_group': '19200.bl', 'aut_hash': 2982525735421943295, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 19200, 'aut_permdeg': 60, 'aut_perms': [8136874713246293763028497455606133068975708175648154763617858347622586682103005958, 6934399733922168734830522176859428247185312012111764315341458790879842728025851968, 3585945862020465654294923165798376508948739708372165928075095220210330634674726950, 3469616905819887784167655654387671303371458314352926508957675478632946355614950828, 3289900345393565223160298986657818362770277107493915736004796806720749786489121159, 5733067168724606345852653127105550383984186449035351548128565875507411378535647252], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 6, 1], [2, 25, 1, 2], [4, 25, 2, 2], [4, 50, 6, 1], [5, 8, 3, 1], [10, 8, 3, 1], [10, 40, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_5^2.C_2^3.S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '2400.dc', 'autcentquo_hash': 4785015580083470286, 'autcentquo_nilpotent': False, 'autcentquo_order': 2400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_5^2:\\Unitary(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 10, 6], [2, 25, 2], [4, 25, 4], [4, 50, 6], [5, 8, 3], [10, 8, 3], [10, 40, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '400.207', 'commutator_count': 1, 'commutator_label': '50.4', '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': 1194, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['400.207', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 6], [2, 25, 1, 2], [4, 25, 2, 2], [4, 50, 1, 6], [5, 8, 1, 3], [10, 8, 1, 3], [10, 40, 1, 6]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 6562080, 'exponent': 20, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '800.1194', 'hash': 1194, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 2, 5, 5, 4, 1], 'inner_gens': [[1563129, 969393, 1125673, 625641, 547501, 1172503, 1565004], [1563139, 1047513, 1453857, 547521, 703751, 1172518, 1565004], [1719389, 1219392, 891283, 625641, 469391, 1406893, 1565004], [1641259, 1125633, 969413, 547511, 625626, 1485023, 1565004], [1875629, 891263, 1125673, 547511, 625626, 1250628, 1565004], [1563129, 891273, 969413, 703771, 469376, 1172503, 1565004], [1563129, 1047513, 891283, 547511, 625626, 1172503, 1565004]], 'inner_hash': 207, 'inner_nilpotent': False, 'inner_order': 400, 'inner_split': False, 'inner_tex': 'D_5^2.C_2^2', 'inner_used': [1, 2, 3, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 4], [8, 12]], 'label': '800.1194', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'D5^2.C2^3', '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': 11, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 32, 'number_divisions': 30, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': 62, 'number_subgroup_classes': 245, 'number_subgroups': 2726, 'old_label': None, 'order': 800, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 111], [4, 400], [5, 24], [10, 264]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [1375747, 1563139, 391251, 1563139, 391251], 'outer_gens': [[1797509, 861923, 891283, 547511, 391271, 1328773, 1565004], [1563134, 1047503, 1455742, 469381, 703751, 783757, 1565004], [1641274, 940028, 406879, 703761, 391256, 1485008, 1565004], [1563144, 1047508, 1299482, 703771, 469376, 1172513, 1565004], [1563149, 1377507, 1221352, 625641, 547501, 1172508, 1565004]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [143, 127, 576, 126, 121], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [4, 2], [8, 12]], 'representations': {'PC': {'code': 186000781532936638637572961003986549088204289965755474804787, 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 2, 2, 5, 2, 5, 36, 9747, 9306, 1641, 80, 16804, 851, 578, 17477, 5052, 7579, 3806, 124, 1574, 11773, 7860, 3947]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1563129, 1047513, 891283, 547511, 625626, 1172503, 1565004]}, 'Perm': {'d': 12, 'gens': [504967, 28374, 41091409, 1, 1640886, 91630134, 136268880]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_5^2.C_2^3', 'transitive_degree': 20, '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: 144434673
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1194, 'group_order': 800, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 391251, 'size': 1}
  • id: 144434684
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1194, 'group_order': 800, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1565004, 'size': 1}
  • id: 144434695
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 3, 'group_counter': 1194, 'group_order': 800, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1219477, 'size': 10}
  • id: 144434699
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 4, 'group_counter': 1194, 'group_order': 800, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1565061, 'size': 10}
  • id: 144434700
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 5, 'group_counter': 1194, 'group_order': 800, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1703751, 'size': 10}
  • id: 144434701
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 6, 'group_counter': 1194, 'group_order': 800, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 391339, 'size': 10}
  • id: 144434702
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 7, 'group_counter': 1194, 'group_order': 800, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 1705641, 'size': 10}
  • id: 144434703
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 8, 'group_counter': 1194, 'group_order': 800, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 1049408, 'size': 10}
  • id: 144434704
    {'aut_label': '2H', 'centralizer': '25.a1', 'counter': 9, 'group_counter': 1194, 'group_order': 800, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 393126, 'size': 25}
  • id: 144434674
    {'aut_label': '2I', 'centralizer': '25.a1', 'counter': 10, 'group_counter': 1194, 'group_order': 800, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 1563129, 'size': 25}
  • id: 144434675
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 11, 'group_counter': 1194, 'group_order': 800, 'label': '4A1', 'order': 4, 'powers': [10, 11], 'representative': 781877, 'size': 25}
  • id: 144434676
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 12, 'group_counter': 1194, 'group_order': 800, 'label': '4A-1', 'order': 4, 'powers': [10, 12], 'representative': 1172503, 'size': 25}
  • id: 144434677
    {'aut_label': '4A-1', 'centralizer': '25.a1', 'counter': 13, 'group_counter': 1194, 'group_order': 800, 'label': '4B1', 'order': 4, 'powers': [10, 13], 'representative': 783752, 'size': 25}
  • id: 144434678
    {'aut_label': '4A1', 'centralizer': '25.a1', 'counter': 14, 'group_counter': 1194, 'group_order': 800, 'label': '4B-1', 'order': 4, 'powers': [10, 14], 'representative': 1174378, 'size': 25}
  • id: 144434679
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 15, 'group_counter': 1194, 'group_order': 800, 'label': '4C', 'order': 4, 'powers': [10, 15], 'representative': 1219387, 'size': 50}
  • id: 144434680
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 16, 'group_counter': 1194, 'group_order': 800, 'label': '4D', 'order': 4, 'powers': [10, 16], 'representative': 1328872, 'size': 50}
  • id: 144434681
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 17, 'group_counter': 1194, 'group_order': 800, 'label': '4E', 'order': 4, 'powers': [10, 17], 'representative': 1299382, 'size': 50}
  • id: 144434682
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 18, 'group_counter': 1194, 'group_order': 800, 'label': '4F', 'order': 4, 'powers': [10, 18], 'representative': 1940071, 'size': 50}
  • id: 144434683
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 19, 'group_counter': 1194, 'group_order': 800, 'label': '4G', 'order': 4, 'powers': [10, 19], 'representative': 1018153, 'size': 50}
  • id: 144434685
    {'aut_label': '4C', 'centralizer': '50.a1', 'counter': 20, 'group_counter': 1194, 'group_order': 800, 'label': '4H', 'order': 4, 'powers': [10, 20], 'representative': 1781941, 'size': 50}
  • id: 144434686
    {'aut_label': '5A', 'centralizer': '8.e1', 'counter': 21, 'group_counter': 1194, 'group_order': 800, 'label': '5A', 'order': 5, 'powers': [21, 1], 'representative': 625626, 'size': 8}
  • id: 144434687
    {'aut_label': '5A', 'centralizer': '8.e1', 'counter': 22, 'group_counter': 1194, 'group_order': 800, 'label': '5B', 'order': 5, 'powers': [22, 1], 'representative': 391266, 'size': 8}
  • id: 144434688
    {'aut_label': '5A', 'centralizer': '8.e1', 'counter': 23, 'group_counter': 1194, 'group_order': 800, 'label': '5C', 'order': 5, 'powers': [23, 1], 'representative': 625641, 'size': 8}
  • id: 144434689
    {'aut_label': '10A', 'centralizer': '8.e1', 'counter': 24, 'group_counter': 1194, 'group_order': 800, 'label': '10A', 'order': 10, 'powers': [21, 2], 'representative': 1643129, 'size': 8}
  • id: 144434690
    {'aut_label': '10A', 'centralizer': '8.e1', 'counter': 25, 'group_counter': 1194, 'group_order': 800, 'label': '10B', 'order': 10, 'powers': [22, 2], 'representative': 1565009, 'size': 8}
  • id: 144434691
    {'aut_label': '10A', 'centralizer': '8.e1', 'counter': 26, 'group_counter': 1194, 'group_order': 800, 'label': '10C', 'order': 10, 'powers': [23, 2], 'representative': 1643134, 'size': 8}
  • id: 144434692
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 27, 'group_counter': 1194, 'group_order': 800, 'label': '10D', 'order': 10, 'powers': [23, 3], 'representative': 1297607, 'size': 40}
  • id: 144434693
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 28, 'group_counter': 1194, 'group_order': 800, 'label': '10E', 'order': 10, 'powers': [22, 4], 'representative': 1877566, 'size': 40}
  • id: 144434694
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 29, 'group_counter': 1194, 'group_order': 800, 'label': '10F', 'order': 10, 'powers': [21, 5], 'representative': 1938146, 'size': 40}
  • id: 144434696
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 30, 'group_counter': 1194, 'group_order': 800, 'label': '10G', 'order': 10, 'powers': [22, 6], 'representative': 547579, 'size': 40}
  • id: 144434697
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 31, 'group_counter': 1194, 'group_order': 800, 'label': '10H', 'order': 10, 'powers': [21, 7], 'representative': 1627516, 'size': 40}
  • id: 144434698
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 32, 'group_counter': 1194, 'group_order': 800, 'label': '10I', 'order': 10, 'powers': [23, 8], 'representative': 815043, 'size': 40}
• 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: 14059284
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1a', '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], 'schur_index': 1}
  • id: 14059295
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1b', '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], 'schur_index': 1}
  • id: 14059306
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1c', '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], 'schur_index': 1}
  • id: 14059308
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1d', '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], 'schur_index': 1}
  • id: 14059309
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1e', '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], 'schur_index': 1}
  • id: 14059310
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1f', '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], 'schur_index': 1}
  • id: 14059311
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1g', '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], 'schur_index': 1}
  • id: 14059312
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1h', '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], 'schur_index': 1}
  • id: 14059313
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1i', '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], 'schur_index': 1}
  • id: 14059285
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1j', '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], 'schur_index': 1}
  • id: 14059286
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1k', '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], 'schur_index': 1}
  • id: 14059287
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1l', '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], 'schur_index': 1}
  • id: 14059288
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1m', '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], 'schur_index': 1}
  • id: 14059289
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1n', '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], 'schur_index': 1}
  • id: 14059290
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1o', '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], 'schur_index': 1}
  • id: 14059291
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.1p', '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], 'schur_index': 1}
  • id: 14059292
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.2a', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14059293
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.2b', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14059294
    {'cdim': 8, 'counter': 19, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8a', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, 3, -2, -2, 0, 0, 0, -1, 0, -1], 'schur_index': 1}
  • id: 14059296
    {'cdim': 8, 'counter': 20, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8b', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, -2, 3, -1, 0, -1, 0, 0, 0], 'schur_index': 1}
  • id: 14059297
    {'cdim': 8, 'counter': 21, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8c', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, -2, 3, -2, 0, -1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 14059298
    {'cdim': 8, 'counter': 22, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8d', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, -2, 3, -2, 0, 1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 14059299
    {'cdim': 8, 'counter': 23, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8e', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, -2, 3, 1, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 14059300
    {'cdim': 8, 'counter': 24, 'faithful': False, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8f', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, 3, -2, -2, 0, 0, 0, 1, 0, 1], 'schur_index': 1}
  • id: 14059301
    {'cdim': 8, 'counter': 25, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8g', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 2, -3, 2, 0, -1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 14059302
    {'cdim': 8, 'counter': 26, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8h', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, 2, 2, -3, 1, 0, -1, 0, 0, 0], 'schur_index': 1}
  • id: 14059303
    {'cdim': 8, 'counter': 27, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8i', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -3, 2, 2, 0, 0, 0, -1, 0, 1], 'schur_index': 1}
  • id: 14059304
    {'cdim': 8, 'counter': 28, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8j', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -3, 2, 2, 0, 0, 0, 1, 0, -1], 'schur_index': 1}
  • id: 14059305
    {'cdim': 8, 'counter': 29, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8k', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, 2, 2, -3, -1, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 14059307
    {'cdim': 8, 'counter': 30, 'faithful': True, 'group': '800.1194', 'group_order': 800, 'image': None, 'label': '800.1194.8l', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, -8, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 2, -3, 2, 0, 1, 0, 0, -1, 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: 33423893
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 800, 'label': '800.1194.1a', '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]]]}
  • id: 33423904
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1b', '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]]]}
  • id: 33423915
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1c', '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]]]}
  • id: 33423919
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1d', '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]]]}
  • id: 33423920
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1e', '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]]]}
  • id: 33423921
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1f', '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]]]}
  • id: 33423922
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1g', '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]]]}
  • id: 33423923
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1h', '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]]]}
  • id: 33423924
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 400, 'label': '800.1194.1i', '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]]]}
  • id: 33423894
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 400, 'label': '800.1194.1j', '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]]]}
  • id: 33423895
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1194.1k', '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]]]}
  • id: 33423896
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1194.1l', '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]]]}
  • id: 33423897
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 400, 'label': '800.1194.1m', '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]]]}
  • id: 33423898
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 400, 'label': '800.1194.1n', '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]]]}
  • id: 33423899
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 400, 'label': '800.1194.1o', '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]]]}
  • id: 33423900
    {'center': '1.a1', 'center_index': 1, 'center_order': 800, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 400, 'label': '800.1194.1p', '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]]]}
  • id: 33423901
    {'center': '4.b1', 'center_index': 4, 'center_order': 200, 'counter': 17, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 50, 'label': '800.1194.2a1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423902
    {'center': '4.b1', 'center_index': 4, 'center_order': 200, 'counter': 18, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 50, 'label': '800.1194.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423903
    {'center': '4.b1', 'center_index': 4, 'center_order': 200, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1', 'kernel_order': 50, 'label': '800.1194.2b1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423905
    {'center': '4.b1', 'center_index': 4, 'center_order': 200, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1', 'kernel_order': 50, 'label': '800.1194.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423906
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8a', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 33423907
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8b', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 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]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423908
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8c', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 33423909
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8d', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 33423910
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8e', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 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]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423911
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 2, 'label': '800.1194.8f', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 33423912
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8g', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 33423913
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8h', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423914
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8i', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 33423916
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8j', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 33423917
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8k', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33423918
    {'center': '400.a1', 'center_index': 400, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '800.1194', 'group_counter': 1194, 'group_order': 800, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 1, 'label': '800.1194.8l', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 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: 116061916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 800, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '800.1194.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '800.1194', 'subgroup_hash': 1194, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 116061927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.2.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: 116061938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.211', 'subgroup_hash': 211, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 116061949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 400, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.212', 'subgroup_hash': 212, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 116061960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '800.1194.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.207', 'subgroup_hash': 207, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 116061971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.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: 116061975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 200, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.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': '4.2', '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': '200.47', 'subgroup_hash': 47, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.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': False, '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: 116061977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.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': ['C2'], '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: 116061917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.43', 'subgroup_hash': 43, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 116061918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.44', 'subgroup_hash': 44, 'subgroup_order': 200, 'subgroup_tex': 'C_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 116061919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 100, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', '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': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 116061920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.8.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': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 116061921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.8.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': '8.5', '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': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', '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': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 50, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 116061924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 116061925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.10.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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: 116061926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': True, 'core_order': 50, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.16.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': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], '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: 116061928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 50, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 116061929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 50, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '800.1194.16.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': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], '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: 116061930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 25, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.20.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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: 116061932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.20.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.20.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: 116061935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '800.1194.25.a1', 'maximal': True, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 116061936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': True, 'core_order': 25, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '800.1194.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'D2', 'C5'], '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: 116061937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 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: 116061939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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: 116061940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 116061941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.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: 116061942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.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: 116061943
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.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': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061944
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.40.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': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.50.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: 116061946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.50.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 116061947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.50.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 116061948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.50.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 116061950
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.80.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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: 116061951
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.80.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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: 116061952
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.80.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061953
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.80.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 116061954
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.80.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: 116061955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.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: 116061956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 116061957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.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: 116061958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.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: 116061959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 116061961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.100.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 116061962
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 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: 116061963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.200.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 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: 116061964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.200.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: 116061965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.200.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: 116061966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '800.1194.200.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: 116061967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.200.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 116061968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.200.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 116061969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '800.1194.400.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': '400.207', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 207, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5^2.C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], '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: 116061970
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.400.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: 116061972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.400.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: 116061973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '800.1194.400.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: 116061974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '800.1194', 'ambient_counter': 1194, 'ambient_order': 800, 'ambient_tex': 'D_5^2.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '800.1194.800.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': '800.1194', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1194, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5^2.C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D3', 'C6'], '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: 116061937
    {'ambient': '800.1194', 'aut_centralizer_order': 80, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2400, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.e1', '20.a1'], 'contains': ['80.a1', '80.b1', '200.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1722, -1, 2820, -1], 'generators': [719384, 703751, 1565004], 'label': '800.1194.40.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.a1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 116061959
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '100.e1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '8.3', 'aut_weyl_index': 2400, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '50.b1', '50.d1'], 'contains': ['200.d1', '200.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [7938, -1, 8480, -1], 'generators': [391344, 641344, 1875649], 'label': '800.1194.100.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.e1', 'projective_image': '800.1194', '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': '4.2'}
  • id: 116061916
    {'ambient': '800.1194', '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': '400.a1', 'complements': ['800.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '25.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8256, 3900, 7366, 4198], 'generators': [391271, 1047513, 891283, 1172503, 1875629, 703751, 1565004], 'label': '800.1194.1.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': '400.207', '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': '400.207'}
  • id: 116061917
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 12, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 24, 'centralizer': '400.a1', 'complements': ['200.a1', '200.c1'], 'conjugacy_class_count': 12, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.b1', '8.d1', '100.e1'], 'core': '4.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [7933, 2310, 7126, 2487], 'generators': [547579, 391271, 641344, 1875629, 703751], 'label': '800.1194.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.b1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061918
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': ['200.a1', '200.c1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.d1'], 'contains': ['8.d1', '100.f1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [9299, 919, 8195, 989], 'generators': [391271, 1047513, 641344, 1875629, 703751], 'label': '800.1194.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.c1', '2.d1'], 'normal_contains': ['8.d1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061919
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.b1', '16.c1', '40.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1303, 6434, 2230, 6914], 'generators': [391271, 1875629, 703751, 1565004], 'label': '800.1194.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061920
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '8.b1', 'aut_quo_index': 21, 'aut_stab_index': 6, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 24, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.d1', '4.e1'], 'contains': ['16.c1', '16.d1', '40.e1'], 'core': '8.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4528, 3775, 2866, 4052], 'generators': [719384, 391271, 1875629, 703751], 'label': '800.1194.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.d1', '4.e1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 116061921
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': 7, 'aut_stab_index': 2, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.d1'], 'contains': ['16.c1', '40.f1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5555, 4792, 4174, 5148], 'generators': [391271, 1172503, 1875629, 703751], 'label': '800.1194.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.d1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061922
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 42, 'aut_stab_index': 6, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 24, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '4.d1', '4.e1', '4.f1'], 'contains': ['16.c1', '40.g1'], 'core': '8.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [7609, 2872, 6755, 3080], 'generators': [391271, 641344, 1875629, 703751], 'label': '800.1194.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.d1', '4.e1', '4.f1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061923
    {'ambient': '800.1194', 'aut_centralizer_order': 20, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.203', 'aut_weyl_index': 120, 'centralizer': '80.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1'], 'contains': ['16.a1', '16.d1', '40.a1', '40.b1'], 'core': '16.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2230, -1, 1385, -1], 'generators': [719384, 391271, 703751, 1565004], 'label': '800.1194.8.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.e1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 116061924
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 24, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1'], 'contains': ['16.b1', '16.d1', '40.d1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2921, -1, 753, -1], 'generators': [719384, 471251, 391271, 703751], 'label': '800.1194.8.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.f1', 'projective_image': '800.1194', '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: 116061925
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '80.50', 'aut_weyl_index': 240, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1'], 'contains': ['20.a1', '20.b1', '20.c1', '20.d1', '50.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6281, -1, 5492, -1], 'generators': [813128, 1172503, 625646, 1565004, 1875639], 'label': '800.1194.10.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '10.a1', 'projective_image': '400.207', '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: 116061926
    {'ambient': '800.1194', 'aut_centralizer_order': 200, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.67', 'aut_weyl_index': 200, 'centralizer': '16.a1', 'complements': ['50.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.e1'], 'contains': ['32.a1', '80.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [404, 5519, 1537, 5673], 'generators': [391271, 703751, 1565004], 'label': '800.1194.16.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['32.a1', '400.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '400.207', 'quotient_action_image': '16.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 116061927
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '3200.ih', 'aut_weyl_index': 6, 'centralizer': '400.a1', 'complements': ['400.b1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '10.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5979, 7036, 5085, 7574], 'generators': [391271, 1047513, 1172503, 1875629, 703751, 1565004], 'label': '800.1194.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '400.207', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061928
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': ['50.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.f1'], 'contains': ['32.a1', '80.d1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1119, 6849, 188, 7104], 'generators': [471251, 391271, 703751], 'label': '800.1194.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '800.1194', 'quotient_action_image': '16.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061929
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '16.c1', 'aut_quo_index': 420, 'aut_stab_index': 1, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '80.e1'], 'core': '16.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4735, 4190, 3925, 4242], 'generators': [391271, 1875629, 703751], 'label': '800.1194.16.c1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061930
    {'ambient': '800.1194', 'aut_centralizer_order': 20, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '80.30', 'aut_weyl_index': 240, 'centralizer': '80.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '8.e1', '8.f1'], 'contains': ['32.a1', '80.b1', '80.c1'], 'core': '32.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2425, -1, 774, -1], 'generators': [719384, 391271, 703751], 'label': '800.1194.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.d1', 'projective_image': '800.1194', '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': '40.12'}
  • id: 116061931
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '10.a1'], 'contains': ['40.a1', '40.b1', '40.c1', '40.d1', '40.e1', '100.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3412, -1, 3482, -1], 'generators': [625646, 1875629, 406879, 1565004], 'label': '800.1194.20.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.a1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 116061932
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '10.a1'], 'contains': ['40.c1', '40.f1', '100.b1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5309, -1, 4805, -1], 'generators': [1563129, 391271, 1172503, 1565004], 'label': '800.1194.20.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.b1', 'projective_image': '400.207', '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: 116061933
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '10.a1'], 'contains': ['40.c1', '40.g1', '100.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6493, -1, 6180, -1], 'generators': [641344, 1875649, 1565004, 703771], 'label': '800.1194.20.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.c1', 'projective_image': '400.207', '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: 116061934
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.d1', '10.a1'], 'contains': ['40.e1', '40.f1', '40.g1', '100.d1'], 'core': '800.a1', 'coset_action_label': '20T154', 'count': 120, 'diagramx': [7246, -1, 5492, -1], 'generators': [813128, 1172503, 625646, 1875639], 'label': '800.1194.20.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.d1', 'projective_image': '800.1194', '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: 116061935
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '192.1538', 'aut_weyl_index': 100, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['50.a1', '50.b1', '50.c1', '50.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8752, -1, 8908, -1], 'generators': [1563129, 813128, 1172503, 1565004, 813153], 'label': '800.1194.25.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': '400.207', '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': '4.2'}
  • id: 116061936
    {'ambient': '800.1194', 'aut_centralizer_order': 200, 'aut_label': '32.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '96.67', 'aut_weyl_index': 200, 'centralizer': '16.a1', 'complements': ['25.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'contains': ['160.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [661, 5519, 1537, 5673], 'generators': [391271, 703751], 'label': '800.1194.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '800.1194', 'quotient_action_image': '16.13', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 116061938
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '3200.ga', 'aut_weyl_index': 6, 'centralizer': '400.a1', 'complements': ['400.b1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.e1', '50.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7090, 4980, 6312, 5360], 'generators': [547579, 391271, 641344, 1875629, 703751, 1565004], 'label': '800.1194.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '400.207', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061939
    {'ambient': '800.1194', 'aut_centralizer_order': 80, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 480, 'centralizer': '40.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.e1', '20.a1'], 'contains': ['80.a1', '80.c1', '200.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1019, -1, 3461, -1], 'generators': [625646, 406879, 1565004], 'label': '800.1194.40.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.b1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 116061940
    {'ambient': '800.1194', 'aut_centralizer_order': 32, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '20.a1', '20.b1', '20.c1'], 'contains': ['80.a1', '80.d1', '80.e1', '200.b1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2425, -1, 4841, -1], 'generators': [391271, 1875629, 1565004], 'label': '800.1194.40.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.c1', 'projective_image': '400.207', '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': '20.3'}
  • id: 116061941
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.f1', '20.a1'], 'contains': ['80.b1', '80.c1', '80.d1', '200.c1'], 'core': '800.a1', 'coset_action_label': '40T722', 'count': 60, 'diagramx': [3172, -1, 2179, -1], 'generators': [471251, 625646, 406879], 'label': '800.1194.40.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.d1', 'projective_image': '800.1194', '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: 116061942
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '20.a1', '20.d1'], 'contains': ['80.b1', '80.c1', '80.e1', '200.d1'], 'core': '800.a1', 'coset_action_label': '40T736', 'count': 60, 'diagramx': [4372, -1, 4388, -1], 'generators': [625646, 1875629, 406879], 'label': '800.1194.40.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.e1', 'projective_image': '800.1194', '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: 116061943
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '20.b1', '20.d1'], 'contains': ['80.e1', '200.e1'], 'core': '800.a1', 'coset_action_label': '40T757', 'count': 60, 'diagramx': [5701, -1, 5671, -1], 'generators': [1563129, 391271, 1172503], 'label': '800.1194.40.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.f1', 'projective_image': '800.1194', '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: 116061944
    {'ambient': '800.1194', 'aut_centralizer_order': 16, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.d1', '20.c1', '20.d1'], 'contains': ['80.e1', '200.f1'], 'core': '800.a1', 'coset_action_label': '40T693', 'count': 60, 'diagramx': [7190, -1, 6037, -1], 'generators': [641344, 1875649, 703771], 'label': '800.1194.40.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.g1', 'projective_image': '800.1194', '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: 116061945
    {'ambient': '800.1194', 'aut_centralizer_order': 32, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2400, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['10.a1', '25.a1'], 'contains': ['100.a1', '100.b1', '100.c1', '100.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6510, -1, 7386, -1], 'generators': [1563129, 813128, 1172503, 1565004], 'label': '800.1194.50.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': '400.207', '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': '2.1'}
  • id: 116061946
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '32.27', 'aut_weyl_index': 600, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '25.a1'], 'contains': ['100.a1', '100.c1', '100.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7759, -1, 8333, -1], 'generators': [391344, 641344, 1875649, 1565004], 'label': '800.1194.50.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': '400.207', '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': '4.2'}
  • id: 116061947
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '96.227', 'aut_weyl_index': 200, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '25.a1'], 'contains': ['100.c1', '100.f1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8954, -1, 9697, -1], 'generators': [641344, 1875649, 1125633, 1565004], 'label': '800.1194.50.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': '400.207', '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': '4.2'}
  • id: 116061948
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '50.d1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '24.12', 'aut_weyl_index': 800, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.d1', '25.a1'], 'contains': ['100.d1', '100.e1', '100.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [9596, -1, 8918, -1], 'generators': [1563129, 813128, 1172503, 1221352], 'label': '800.1194.50.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': '800.1194', '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': '4.2'}
  • id: 116061949
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '9600.cj', 'aut_weyl_index': 2, 'centralizer': '400.a1', 'complements': ['400.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.f1', '50.c1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8256, 2809, 8317, 3024], 'generators': [391271, 1047513, 641344, 1875629, 703751, 1565004], 'label': '800.1194.2.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': '400.207', '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': '400.207'}
  • id: 116061950
    {'ambient': '800.1194', 'aut_centralizer_order': 800, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '40.a1', '40.b1', '40.c1'], 'contains': ['160.a1', '400.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1052, -1, 3497, -1], 'generators': [391271, 1565004], 'label': '800.1194.80.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.a1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 116061951
    {'ambient': '800.1194', 'aut_centralizer_order': 80, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.d1', '40.a1', '40.d1', '40.e1'], 'contains': ['160.a1', '400.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2642, -1, 2683, -1], 'generators': [719384, 703751], 'label': '800.1194.80.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 116061952
    {'ambient': '800.1194', 'aut_centralizer_order': 80, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '40.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.d1', '40.b1', '40.d1', '40.e1'], 'contains': ['160.a1', '400.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3513, -1, 3090, -1], 'generators': [625646, 406879], 'label': '800.1194.80.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.c1', 'projective_image': '800.1194', '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': '20.3'}
  • id: 116061953
    {'ambient': '800.1194', 'aut_centralizer_order': 32, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.b1', '40.c1', '40.d1'], 'contains': ['160.a1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1933, -1, 2275, -1], 'generators': [471251, 391271], 'label': '800.1194.80.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.d1', 'projective_image': '800.1194', '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': '20.3'}
  • id: 116061954
    {'ambient': '800.1194', 'aut_centralizer_order': 32, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '20.3', 'aut_weyl_index': 960, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.c1', '40.c1', '40.e1', '40.f1', '40.g1'], 'contains': ['160.a1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4903, -1, 4775, -1], 'generators': [391271, 1875629], 'label': '800.1194.80.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.e1', 'projective_image': '800.1194', '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: 116061955
    {'ambient': '800.1194', 'aut_centralizer_order': 64, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['20.a1', '50.a1', '50.b1'], 'contains': ['200.a1', '200.b1', '200.c1', '200.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3999, -1, 5279, -1], 'generators': [563134, 1875634, 1565004], 'label': '800.1194.100.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': '400.207', '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': '2.1'}
  • id: 116061956
    {'ambient': '800.1194', 'aut_centralizer_order': 384, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1', '50.a1'], 'contains': ['200.b1', '200.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5387, -1, 6567, -1], 'generators': [1563129, 1172503, 1565004], 'label': '800.1194.100.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.b1', 'projective_image': '400.207', '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: 116061957
    {'ambient': '800.1194', 'aut_centralizer_order': 64, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': 75, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4800, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['20.c1', '50.a1', '50.b1', '50.c1'], 'contains': ['200.b1', '200.f1'], 'core': '400.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6599, -1, 7951, -1], 'generators': [641344, 1875649, 1565004], 'label': '800.1194.100.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': '400.207', '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': '2.1'}
  • id: 116061958
    {'ambient': '800.1194', 'aut_centralizer_order': 32, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': 300, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['20.d1', '50.a1', '50.d1'], 'contains': ['200.d1', '200.e1', '200.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [7357, -1, 7259, -1], 'generators': [1563129, 813128, 1172503], 'label': '800.1194.100.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': '800.1194', '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': '2.1'}
  • id: 116061960
    {'ambient': '800.1194', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': ['400.a1', '400.c1', '400.b1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.f1', '50.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [9299, 867, 7366, 933], 'generators': [1047513, 391271, 1533872, 1172503, 1875629, 703751], 'label': '800.1194.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '800.1194', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061961
    {'ambient': '800.1194', 'aut_centralizer_order': 8, 'aut_label': '100.f1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '24.12', 'aut_weyl_index': 800, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '50.c1', '50.d1'], 'contains': ['200.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [9277, -1, 9086, -1], 'generators': [641344, 1875649, 1125633], 'label': '800.1194.100.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': '800.1194', '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': '4.2'}
  • id: 116061962
    {'ambient': '800.1194', 'aut_centralizer_order': 800, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4800, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['32.a1', '80.a1', '80.b1', '80.c1', '80.d1', '80.e1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1933, -1, 3090, -1], 'generators': [391271], 'label': '800.1194.160.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '160.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 116061963
    {'ambient': '800.1194', 'aut_centralizer_order': 320, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '10.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['40.a1', '40.b1', '100.a1'], 'contains': ['400.a1', '400.b1'], 'core': '400.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2023, -1, 4347, -1], 'generators': [563134, 1565004], 'label': '800.1194.200.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '200.a1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 116061964
    {'ambient': '800.1194', 'aut_centralizer_order': 768, 'aut_label': '200.b1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1', '100.a1', '100.b1', '100.c1'], 'contains': ['400.a1', '400.c1', '400.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3999, -1, 5167, -1], 'generators': [1875629, 1565004], 'label': '800.1194.200.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.b1', 'projective_image': '400.207', '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: 116061965
    {'ambient': '800.1194', 'aut_centralizer_order': 64, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['40.d1', '100.a1'], 'contains': ['400.b1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3195, -1, 3930, -1], 'generators': [471271, 563134], 'label': '800.1194.200.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1', 'old_label': '200.c1', 'projective_image': '800.1194', '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: 116061966
    {'ambient': '800.1194', 'aut_centralizer_order': 64, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['40.e1', '100.a1', '100.d1', '100.e1'], 'contains': ['400.b1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4540, -1, 5584, -1], 'generators': [563134, 1875634], 'label': '800.1194.200.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.d1', 'projective_image': '800.1194', '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': '2.1'}
  • id: 116061967
    {'ambient': '800.1194', 'aut_centralizer_order': 384, 'aut_label': '200.e1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.f1', '100.b1', '100.d1'], 'contains': ['400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5639, -1, 6271, -1], 'generators': [1563129, 1172503], 'label': '800.1194.200.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.e1', 'projective_image': '800.1194', '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: 116061968
    {'ambient': '800.1194', 'aut_centralizer_order': 64, 'aut_label': '200.f1', 'aut_quo_index': None, 'aut_stab_index': 150, 'aut_weyl_group': '2.1', 'aut_weyl_index': 9600, 'centralizer': '50.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['40.g1', '100.c1', '100.d1', '100.e1', '100.f1'], 'contains': ['400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7770, -1, 7605, -1], 'generators': [641344, 1875649], 'label': '800.1194.200.f1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.f1', 'projective_image': '800.1194', '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': '2.1'}
  • id: 116061969
    {'ambient': '800.1194', 'aut_centralizer_order': 19200, 'aut_label': '400.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '1.a1', 'complements': ['2.d1'], 'conjugacy_class_count': 1, 'contained_in': ['80.a1', '200.a1', '200.b1'], 'contains': ['800.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2201, 9133, 4347, 8904], 'generators': [1565004], 'label': '800.1194.400.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '400.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '400.a1', 'projective_image': '400.207', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.207', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 116061970
    {'ambient': '800.1194', 'aut_centralizer_order': 320, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '10.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['80.b1', '80.c1', '200.a1', '200.c1', '200.d1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2782, -1, 3981, -1], 'generators': [563134], 'label': '800.1194.400.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '400.b1', 'projective_image': '800.1194', '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: 116061971
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 12, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.e1', '8.f1', '20.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3412, 6610, 2866, 7116], 'generators': [719384, 391271, 1875629, 703751, 1565004], 'label': '800.1194.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '400.207', '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': '400.207'}
  • id: 116061972
    {'ambient': '800.1194', 'aut_centralizer_order': 768, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1', '200.b1', '200.c1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3190, -1, 3614, -1], 'generators': [471251], 'label': '800.1194.400.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.c1', 'projective_image': '800.1194', '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: 116061973
    {'ambient': '800.1194', 'aut_centralizer_order': 768, 'aut_label': '400.d1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 19200, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1', '200.b1', '200.d1', '200.e1', '200.f1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [4719, -1, 5375, -1], 'generators': [1875629], 'label': '800.1194.400.d1', 'mobius_quo': None, 'mobius_sub': -64, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.d1', 'projective_image': '800.1194', '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: 116061974
    {'ambient': '800.1194', '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', '400.a1', '400.b1', '400.c1', '400.d1'], 'contains': [], 'core': '800.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2782, 9133, 3981, 8904], 'generators': [], 'label': '800.1194.800.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '800.a1', 'normal_contained_in': ['32.a1', '400.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '800.a1', 'projective_image': '800.1194', '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: 116061975
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.c1', '20.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5226, 8407, 4148, 9049], 'generators': [391271, 1172503, 1875629, 703751, 1565004], 'label': '800.1194.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061976
    {'ambient': '800.1194', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 12, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.d1', '20.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6526, 4928, 6312, 5304], 'generators': [391271, 641344, 1875629, 703751, 1565004], 'label': '800.1194.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '400.207', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 116061977
    {'ambient': '800.1194', 'aut_centralizer_order': 2, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 12, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 24, 'centralizer': '400.a1', 'complements': ['200.a1', '200.c1'], 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.b1', '8.c1', '8.d1', '20.d1'], 'core': '4.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [7246, 3588, 4861, 3862], 'generators': [391271, 1047513, 1172503, 1875629, 703751], 'label': '800.1194.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.b1', '8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '800.1194', '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': '400.207'}