Abstract group data - 1680.826

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 10, 12, 12, 70, 12, 10], 'aut_gens': [[1, 2, 4], [469, 1150, 988], [205, 86, 1564], [1369, 1010, 628], [1477, 1318, 988], [889, 1570, 284], [1669, 310, 1132], [769, 1010, 1564]], 'aut_group': None, 'aut_hash': 1251946377977758017, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 80640, 'aut_permdeg': 102, 'aut_perms': [488464477062996874895635079428116449081790845406286207727993546787589774402760140433173772668249010499808558515436796049528844004559937306258142064288534110211506, 670968861159163472376660917209905895152903926969660636875493308274316928944714057359952606560619696925339193191334296797503305394157281100502302169879645684659767, 726893673845989750984282119725323171136666420273602687626592548982845307682005086848866075815709524017453909617849188641135937463970774619580648994773652862787713, 797124460801477052699680597639338840370616692296152008102704739170724973636615316441276512967118587780403030048414475484275913405128260213888391165962426395856220, 19993781696494542394047960515945659438893110995668203224771396625487580029295472538465285429518249713572149534398698198169341489561363173546655501038391884550753, 505779621915328297002524379451866480165626632002905981004703486618626833275927729781660553716028224057346815065831072023193471504423376967250923684893375374977704, 814226471218431203555732201244837700057231160597551943718729127444288730237353582805305827003284091610770613685989550924180134997060762552391303324710103966988733], 'aut_phi_ratio': 210.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 21, 2, 1], [2, 30, 2, 1], [2, 70, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [6, 140, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [10, 42, 4, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 60, 6, 1], [15, 4, 2, 1], [20, 2, 4, 1], [20, 42, 4, 1], [21, 4, 3, 1], [28, 4, 3, 1], [30, 4, 2, 1], [35, 4, 6, 1], [42, 4, 3, 1], [60, 4, 4, 1], [70, 4, 6, 1], [84, 4, 6, 1], [105, 4, 12, 1], [140, 4, 12, 1], [210, 4, 12, 1], [420, 4, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{210}.C_6.C_2^6', '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': 420, 'autcentquo_group': None, 'autcentquo_hash': 2285439238770837057, 'autcentquo_nilpotent': False, 'autcentquo_order': 10080, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 21, 2], [2, 30, 2], [2, 70, 2], [3, 2, 1], [4, 2, 1], [4, 42, 1], [5, 2, 2], [6, 2, 1], [6, 140, 2], [7, 2, 3], [10, 2, 2], [10, 42, 4], [12, 4, 1], [14, 2, 3], [14, 60, 6], [15, 4, 2], [20, 2, 4], [20, 42, 4], [21, 4, 3], [28, 4, 3], [30, 4, 2], [35, 4, 6], [42, 4, 3], [60, 4, 4], [70, 4, 6], [84, 4, 6], [105, 4, 12], [140, 4, 12], [210, 4, 12], [420, 4, 24]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '840.175', 'commutator_count': 1, 'commutator_label': '210.12', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 826, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 21, 1, 2], [2, 30, 1, 2], [2, 70, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [6, 140, 1, 2], [7, 2, 3, 1], [10, 2, 2, 1], [10, 42, 2, 2], [12, 4, 1, 1], [14, 2, 3, 1], [14, 60, 3, 2], [15, 4, 2, 1], [20, 2, 4, 1], [20, 42, 4, 1], [21, 4, 3, 1], [28, 4, 3, 1], [30, 4, 2, 1], [35, 4, 6, 1], [42, 4, 3, 1], [60, 4, 4, 1], [70, 4, 6, 1], [84, 4, 6, 1], [105, 4, 12, 1], [140, 4, 12, 1], [210, 4, 12, 1], [420, 4, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 16128, 'exponent': 420, 'exponents_of_order': [4, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[4, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '840.175', 'hash': 826, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 2, 210], 'inner_gens': [[1, 2, 556], [1, 2, 956], [1129, 730, 4]], 'inner_hash': 175, 'inner_nilpotent': False, 'inner_order': 840, 'inner_split': True, 'inner_tex': 'C_{30}:D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 96, 'irrQ_dim': 96, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 34], [4, 96]], 'label': '1680.826', 'linC_count': 24, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 144, 'linQ_dim': 14, 'linQ_dim_count': 144, 'linR_count': 528, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C140:D6', '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 35, 'number_conjugacy_classes': 138, 'number_divisions': 38, 'number_normal_subgroups': 51, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 216, 'number_subgroups': 3848, 'old_label': None, 'order': 1680, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 243], [3, 2], [4, 44], [5, 4], [6, 282], [7, 6], [10, 172], [12, 4], [14, 366], [15, 8], [20, 176], [21, 12], [28, 12], [30, 8], [35, 24], [42, 12], [60, 16], [70, 24], [84, 24], [105, 48], [140, 48], [210, 48], [420, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [1260, 0, 0, 0], 'outer_gens': [[421, 422, 4], [841, 2, 4], [1, 2, 1124], [1, 2, 1028]], 'outer_group': '96.220', 'outer_hash': 220, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 13, 'outer_perms': [3628800, 479001600, 42000, 41187], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{12}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 5], [6, 4], [8, 4], [12, 3], [16, 1], [24, 3], [48, 3], [96, 1]], 'representations': {'PC': {'code': 494526771487823591264870554265760185949183581217458747, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -3, -5, -7, 11678, 10047, 58, 31139, 3258, 80, 19044, 8131, 137, 68549, 29244, 250, 70566]}, 'Perm': {'d': 19, 'gens': [357001329489966, 3633961, 17, 7, 43545600, 50520, 7116370137676800]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{140}:D_6', 'transitive_degree': 420, '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: 124366110
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 826, 'group_order': 1680, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 124366160
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 826, 'group_order': 1680, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 840, 'size': 1}
  • id: 124366171
    {'aut_label': '2B', 'centralizer': '21.a1.a1', 'counter': 3, 'group_counter': 826, 'group_order': 1680, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 963, 'size': 21}
  • id: 124366182
    {'aut_label': '2B', 'centralizer': '21.a1.a1', 'counter': 4, 'group_counter': 826, 'group_order': 1680, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 843, 'size': 21}
  • id: 124366193
    {'aut_label': '2D', 'centralizer': '30.a1.a1', 'counter': 5, 'group_counter': 826, 'group_order': 1680, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 1122, 'size': 30}
  • id: 124366204
    {'aut_label': '2D', 'centralizer': '30.a1.b1', 'counter': 6, 'group_counter': 826, 'group_order': 1680, 'label': '2E', 'order': 2, 'powers': [1, 6, 6, 6], 'representative': 1150, 'size': 30}
  • id: 124366215
    {'aut_label': '2F', 'centralizer': '70.a1.b1', 'counter': 7, 'group_counter': 826, 'group_order': 1680, 'label': '2F', 'order': 2, 'powers': [1, 7, 7, 7], 'representative': 1117, 'size': 70}
  • id: 124366226
    {'aut_label': '2F', 'centralizer': '70.a1.a1', 'counter': 8, 'group_counter': 826, 'group_order': 1680, 'label': '2G', 'order': 2, 'powers': [1, 8, 8, 8], 'representative': 289, 'size': 70}
  • id: 124366237
    {'aut_label': '3A', 'centralizer': '2.e1.a1', 'counter': 9, 'group_counter': 826, 'group_order': 1680, 'label': '3A', 'order': 3, 'powers': [9, 1, 9, 9], 'representative': 560, 'size': 2}
  • id: 124366111
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 826, 'group_order': 1680, 'label': '4A', 'order': 4, 'powers': [2, 10, 10, 10], 'representative': 420, 'size': 2}
  • id: 124366122
    {'aut_label': '4B', 'centralizer': '42.b1.a1', 'counter': 11, 'group_counter': 826, 'group_order': 1680, 'label': '4B', 'order': 4, 'powers': [2, 11, 11, 11], 'representative': 1223, 'size': 42}
  • id: 124366133
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 826, 'group_order': 1680, 'label': '5A1', 'order': 5, 'powers': [13, 13, 1, 13], 'representative': 336, 'size': 2}
  • id: 124366144
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 826, 'group_order': 1680, 'label': '5A2', 'order': 5, 'powers': [12, 12, 1, 12], 'representative': 672, 'size': 2}
  • id: 124366154
    {'aut_label': '6A', 'centralizer': '2.e1.a1', 'counter': 14, 'group_counter': 826, 'group_order': 1680, 'label': '6A', 'order': 6, 'powers': [9, 2, 14, 14], 'representative': 280, 'size': 2}
  • id: 124366155
    {'aut_label': '6B', 'centralizer': '140.d1.a1', 'counter': 15, 'group_counter': 826, 'group_order': 1680, 'label': '6B', 'order': 6, 'powers': [9, 7, 15, 15], 'representative': 557, 'size': 140}
  • id: 124366156
    {'aut_label': '6B', 'centralizer': '140.d1.b1', 'counter': 16, 'group_counter': 826, 'group_order': 1680, 'label': '6C', 'order': 6, 'powers': [9, 8, 16, 16], 'representative': 1409, 'size': 140}
  • id: 124366157
    {'aut_label': '7A1', 'centralizer': '2.d1.a1', 'counter': 17, 'group_counter': 826, 'group_order': 1680, 'label': '7A1', 'order': 7, 'powers': [18, 19, 18, 1], 'representative': 240, 'size': 2}
  • id: 124366158
    {'aut_label': '7A1', 'centralizer': '2.d1.a1', 'counter': 18, 'group_counter': 826, 'group_order': 1680, 'label': '7A2', 'order': 7, 'powers': [19, 17, 19, 1], 'representative': 480, 'size': 2}
  • id: 124366159
    {'aut_label': '7A1', 'centralizer': '2.d1.a1', 'counter': 19, 'group_counter': 826, 'group_order': 1680, 'label': '7A3', 'order': 7, 'powers': [17, 18, 17, 1], 'representative': 720, 'size': 2}
  • id: 124366161
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 826, 'group_order': 1680, 'label': '10A1', 'order': 10, 'powers': [12, 21, 2, 21], 'representative': 168, 'size': 2}
  • id: 124366162
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 826, 'group_order': 1680, 'label': '10A3', 'order': 10, 'powers': [13, 20, 2, 20], 'representative': 504, 'size': 2}
  • id: 124366163
    {'aut_label': '10B1', 'centralizer': '42.b1.a1', 'counter': 22, 'group_counter': 826, 'group_order': 1680, 'label': '10B1', 'order': 10, 'powers': [12, 23, 3, 23], 'representative': 1635, 'size': 42}
  • id: 124366164
    {'aut_label': '10B1', 'centralizer': '42.b1.a1', 'counter': 23, 'group_counter': 826, 'group_order': 1680, 'label': '10B3', 'order': 10, 'powers': [13, 22, 3, 22], 'representative': 1299, 'size': 42}
  • id: 124366165
    {'aut_label': '10B1', 'centralizer': '42.b1.a1', 'counter': 24, 'group_counter': 826, 'group_order': 1680, 'label': '10C1', 'order': 10, 'powers': [13, 25, 4, 25], 'representative': 1179, 'size': 42}
  • id: 124366166
    {'aut_label': '10B1', 'centralizer': '42.b1.a1', 'counter': 25, 'group_counter': 826, 'group_order': 1680, 'label': '10C3', 'order': 10, 'powers': [12, 24, 4, 24], 'representative': 171, 'size': 42}
  • id: 124366167
    {'aut_label': '12A', 'centralizer': '4.d1.a1', 'counter': 26, 'group_counter': 826, 'group_order': 1680, 'label': '12A', 'order': 12, 'powers': [14, 10, 26, 26], 'representative': 140, 'size': 4}
  • id: 124366168
    {'aut_label': '14A1', 'centralizer': '2.d1.a1', 'counter': 27, 'group_counter': 826, 'group_order': 1680, 'label': '14A1', 'order': 14, 'powers': [17, 28, 29, 2], 'representative': 120, 'size': 2}
  • id: 124366169
    {'aut_label': '14A1', 'centralizer': '2.d1.a1', 'counter': 28, 'group_counter': 826, 'group_order': 1680, 'label': '14A3', 'order': 14, 'powers': [19, 29, 27, 2], 'representative': 360, 'size': 2}
  • id: 124366170
    {'aut_label': '14A1', 'centralizer': '2.d1.a1', 'counter': 29, 'group_counter': 826, 'group_order': 1680, 'label': '14A5', 'order': 14, 'powers': [18, 27, 28, 2], 'representative': 600, 'size': 2}
  • id: 124366172
    {'aut_label': '14B1', 'centralizer': '60.c1.a1', 'counter': 30, 'group_counter': 826, 'group_order': 1680, 'label': '14B1', 'order': 14, 'powers': [19, 31, 32, 5], 'representative': 1602, 'size': 60}
  • id: 124366173
    {'aut_label': '14B1', 'centralizer': '60.c1.a1', 'counter': 31, 'group_counter': 826, 'group_order': 1680, 'label': '14B3', 'order': 14, 'powers': [18, 32, 30, 5], 'representative': 882, 'size': 60}
  • id: 124366174
    {'aut_label': '14B1', 'centralizer': '60.c1.a1', 'counter': 32, 'group_counter': 826, 'group_order': 1680, 'label': '14B5', 'order': 14, 'powers': [17, 30, 31, 5], 'representative': 162, 'size': 60}
  • id: 124366175
    {'aut_label': '14B1', 'centralizer': '60.c1.b1', 'counter': 33, 'group_counter': 826, 'group_order': 1680, 'label': '14C1', 'order': 14, 'powers': [18, 34, 35, 6], 'representative': 910, 'size': 60}
  • id: 124366176
    {'aut_label': '14B1', 'centralizer': '60.c1.b1', 'counter': 34, 'group_counter': 826, 'group_order': 1680, 'label': '14C3', 'order': 14, 'powers': [17, 35, 33, 6], 'representative': 430, 'size': 60}
  • id: 124366177
    {'aut_label': '14B1', 'centralizer': '60.c1.b1', 'counter': 35, 'group_counter': 826, 'group_order': 1680, 'label': '14C5', 'order': 14, 'powers': [19, 33, 34, 6], 'representative': 1630, 'size': 60}
  • id: 124366178
    {'aut_label': '15A1', 'centralizer': '4.d1.a1', 'counter': 36, 'group_counter': 826, 'group_order': 1680, 'label': '15A1', 'order': 15, 'powers': [37, 12, 9, 37], 'representative': 112, 'size': 4}
  • id: 124366179
    {'aut_label': '15A1', 'centralizer': '4.d1.a1', 'counter': 37, 'group_counter': 826, 'group_order': 1680, 'label': '15A2', 'order': 15, 'powers': [36, 13, 9, 36], 'representative': 224, 'size': 4}
  • id: 124366180
    {'aut_label': '20A1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 826, 'group_order': 1680, 'label': '20A1', 'order': 20, 'powers': [20, 39, 10, 40], 'representative': 84, 'size': 2}
  • id: 124366181
    {'aut_label': '20A1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 826, 'group_order': 1680, 'label': '20A3', 'order': 20, 'powers': [21, 41, 10, 38], 'representative': 252, 'size': 2}
  • id: 124366183
    {'aut_label': '20A1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 826, 'group_order': 1680, 'label': '20A7', 'order': 20, 'powers': [21, 38, 10, 41], 'representative': 588, 'size': 2}
  • id: 124366184
    {'aut_label': '20A1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 826, 'group_order': 1680, 'label': '20A9', 'order': 20, 'powers': [20, 40, 10, 39], 'representative': 756, 'size': 2}
  • id: 124366185
    {'aut_label': '20B1', 'centralizer': '42.b1.a1', 'counter': 42, 'group_counter': 826, 'group_order': 1680, 'label': '20B1', 'order': 20, 'powers': [21, 43, 11, 44], 'representative': 215, 'size': 42}
  • id: 124366186
    {'aut_label': '20B1', 'centralizer': '42.b1.a1', 'counter': 43, 'group_counter': 826, 'group_order': 1680, 'label': '20B3', 'order': 20, 'powers': [20, 45, 11, 42], 'representative': 719, 'size': 42}
  • id: 124366187
    {'aut_label': '20B1', 'centralizer': '42.b1.a1', 'counter': 44, 'group_counter': 826, 'group_order': 1680, 'label': '20B7', 'order': 20, 'powers': [20, 42, 11, 45], 'representative': 47, 'size': 42}
  • id: 124366188
    {'aut_label': '20B1', 'centralizer': '42.b1.a1', 'counter': 45, 'group_counter': 826, 'group_order': 1680, 'label': '20B9', 'order': 20, 'powers': [21, 44, 11, 43], 'representative': 551, 'size': 42}
  • id: 124366189
    {'aut_label': '21A1', 'centralizer': '4.d1.a1', 'counter': 46, 'group_counter': 826, 'group_order': 1680, 'label': '21A1', 'order': 21, 'powers': [47, 17, 47, 9], 'representative': 80, 'size': 4}
  • id: 124366190
    {'aut_label': '21A1', 'centralizer': '4.d1.a1', 'counter': 47, 'group_counter': 826, 'group_order': 1680, 'label': '21A2', 'order': 21, 'powers': [48, 18, 48, 9], 'representative': 160, 'size': 4}
  • id: 124366191
    {'aut_label': '21A1', 'centralizer': '4.d1.a1', 'counter': 48, 'group_counter': 826, 'group_order': 1680, 'label': '21A4', 'order': 21, 'powers': [46, 19, 46, 9], 'representative': 320, 'size': 4}
  • id: 124366192
    {'aut_label': '28A1', 'centralizer': '4.d1.a1', 'counter': 49, 'group_counter': 826, 'group_order': 1680, 'label': '28A1', 'order': 28, 'powers': [27, 50, 51, 10], 'representative': 60, 'size': 4}
  • id: 124366194
    {'aut_label': '28A1', 'centralizer': '4.d1.a1', 'counter': 50, 'group_counter': 826, 'group_order': 1680, 'label': '28A3', 'order': 28, 'powers': [28, 51, 49, 10], 'representative': 180, 'size': 4}
  • id: 124366195
    {'aut_label': '28A1', 'centralizer': '4.d1.a1', 'counter': 51, 'group_counter': 826, 'group_order': 1680, 'label': '28A5', 'order': 28, 'powers': [29, 49, 50, 10], 'representative': 300, 'size': 4}
  • id: 124366196
    {'aut_label': '30A1', 'centralizer': '4.d1.a1', 'counter': 52, 'group_counter': 826, 'group_order': 1680, 'label': '30A1', 'order': 30, 'powers': [36, 20, 14, 53], 'representative': 56, 'size': 4}
  • id: 124366197
    {'aut_label': '30A1', 'centralizer': '4.d1.a1', 'counter': 53, 'group_counter': 826, 'group_order': 1680, 'label': '30A7', 'order': 30, 'powers': [37, 21, 14, 52], 'representative': 392, 'size': 4}
  • id: 124366198
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 54, 'group_counter': 826, 'group_order': 1680, 'label': '35A1', 'order': 35, 'powers': [55, 56, 17, 12], 'representative': 48, 'size': 4}
  • id: 124366199
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 55, 'group_counter': 826, 'group_order': 1680, 'label': '35A2', 'order': 35, 'powers': [57, 54, 18, 13], 'representative': 96, 'size': 4}
  • id: 124366200
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 56, 'group_counter': 826, 'group_order': 1680, 'label': '35A3', 'order': 35, 'powers': [54, 59, 19, 13], 'representative': 144, 'size': 4}
  • id: 124366201
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 57, 'group_counter': 826, 'group_order': 1680, 'label': '35A4', 'order': 35, 'powers': [58, 55, 19, 12], 'representative': 192, 'size': 4}
  • id: 124366202
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 58, 'group_counter': 826, 'group_order': 1680, 'label': '35A8', 'order': 35, 'powers': [59, 57, 17, 13], 'representative': 384, 'size': 4}
  • id: 124366203
    {'aut_label': '35A1', 'centralizer': '4.d1.a1', 'counter': 59, 'group_counter': 826, 'group_order': 1680, 'label': '35A9', 'order': 35, 'powers': [56, 58, 18, 12], 'representative': 432, 'size': 4}
  • id: 124366205
    {'aut_label': '42A1', 'centralizer': '4.d1.a1', 'counter': 60, 'group_counter': 826, 'group_order': 1680, 'label': '42A1', 'order': 42, 'powers': [46, 27, 61, 14], 'representative': 40, 'size': 4}
  • id: 124366206
    {'aut_label': '42A1', 'centralizer': '4.d1.a1', 'counter': 61, 'group_counter': 826, 'group_order': 1680, 'label': '42A5', 'order': 42, 'powers': [47, 29, 62, 14], 'representative': 200, 'size': 4}
  • id: 124366207
    {'aut_label': '42A1', 'centralizer': '4.d1.a1', 'counter': 62, 'group_counter': 826, 'group_order': 1680, 'label': '42A11', 'order': 42, 'powers': [48, 28, 60, 14], 'representative': 440, 'size': 4}
  • id: 124366208
    {'aut_label': '60A1', 'centralizer': '4.d1.a1', 'counter': 63, 'group_counter': 826, 'group_order': 1680, 'label': '60A1', 'order': 60, 'powers': [52, 38, 26, 64], 'representative': 28, 'size': 4}
  • id: 124366209
    {'aut_label': '60A1', 'centralizer': '4.d1.a1', 'counter': 64, 'group_counter': 826, 'group_order': 1680, 'label': '60A7', 'order': 60, 'powers': [53, 40, 26, 65], 'representative': 196, 'size': 4}
  • id: 124366210
    {'aut_label': '60A1', 'centralizer': '4.d1.a1', 'counter': 65, 'group_counter': 826, 'group_order': 1680, 'label': '60A11', 'order': 60, 'powers': [52, 41, 26, 66], 'representative': 308, 'size': 4}
  • id: 124366211
    {'aut_label': '60A1', 'centralizer': '4.d1.a1', 'counter': 66, 'group_counter': 826, 'group_order': 1680, 'label': '60A17', 'order': 60, 'powers': [53, 39, 26, 63], 'representative': 476, 'size': 4}
  • id: 124366212
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 67, 'group_counter': 826, 'group_order': 1680, 'label': '70A1', 'order': 70, 'powers': [54, 68, 27, 20], 'representative': 24, 'size': 4}
  • id: 124366213
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 68, 'group_counter': 826, 'group_order': 1680, 'label': '70A3', 'order': 70, 'powers': [56, 69, 28, 21], 'representative': 72, 'size': 4}
  • id: 124366214
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 69, 'group_counter': 826, 'group_order': 1680, 'label': '70A9', 'order': 70, 'powers': [59, 71, 29, 20], 'representative': 216, 'size': 4}
  • id: 124366216
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 70, 'group_counter': 826, 'group_order': 1680, 'label': '70A11', 'order': 70, 'powers': [57, 72, 28, 20], 'representative': 264, 'size': 4}
  • id: 124366217
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 71, 'group_counter': 826, 'group_order': 1680, 'label': '70A13', 'order': 70, 'powers': [58, 70, 27, 21], 'representative': 312, 'size': 4}
  • id: 124366218
    {'aut_label': '70A1', 'centralizer': '4.d1.a1', 'counter': 72, 'group_counter': 826, 'group_order': 1680, 'label': '70A23', 'order': 70, 'powers': [55, 67, 29, 21], 'representative': 552, 'size': 4}
  • id: 124366219
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 73, 'group_counter': 826, 'group_order': 1680, 'label': '84A1', 'order': 84, 'powers': [60, 49, 75, 26], 'representative': 20, 'size': 4}
  • id: 124366220
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 74, 'group_counter': 826, 'group_order': 1680, 'label': '84A-1', 'order': 84, 'powers': [60, 49, 76, 26], 'representative': 1660, 'size': 4}
  • id: 124366221
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 75, 'group_counter': 826, 'group_order': 1680, 'label': '84A5', 'order': 84, 'powers': [61, 51, 77, 26], 'representative': 100, 'size': 4}
  • id: 124366222
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 76, 'group_counter': 826, 'group_order': 1680, 'label': '84A-5', 'order': 84, 'powers': [61, 51, 78, 26], 'representative': 1580, 'size': 4}
  • id: 124366223
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 77, 'group_counter': 826, 'group_order': 1680, 'label': '84A11', 'order': 84, 'powers': [62, 50, 73, 26], 'representative': 220, 'size': 4}
  • id: 124366224
    {'aut_label': '84A1', 'centralizer': '4.d1.a1', 'counter': 78, 'group_counter': 826, 'group_order': 1680, 'label': '84A-11', 'order': 84, 'powers': [62, 50, 74, 26], 'representative': 1460, 'size': 4}
  • id: 124366225
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 79, 'group_counter': 826, 'group_order': 1680, 'label': '105A1', 'order': 105, 'powers': [81, 54, 46, 36], 'representative': 16, 'size': 4}
  • id: 124366227
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 80, 'group_counter': 826, 'group_order': 1680, 'label': '105A-1', 'order': 105, 'powers': [82, 54, 46, 36], 'representative': 1664, 'size': 4}
  • id: 124366228
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 81, 'group_counter': 826, 'group_order': 1680, 'label': '105A2', 'order': 105, 'powers': [83, 55, 47, 37], 'representative': 32, 'size': 4}
  • id: 124366229
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 82, 'group_counter': 826, 'group_order': 1680, 'label': '105A-2', 'order': 105, 'powers': [84, 55, 47, 37], 'representative': 1648, 'size': 4}
  • id: 124366230
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 83, 'group_counter': 826, 'group_order': 1680, 'label': '105A4', 'order': 105, 'powers': [85, 57, 48, 36], 'representative': 64, 'size': 4}
  • id: 124366231
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 84, 'group_counter': 826, 'group_order': 1680, 'label': '105A-4', 'order': 105, 'powers': [86, 57, 48, 36], 'representative': 1616, 'size': 4}
  • id: 124366232
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 85, 'group_counter': 826, 'group_order': 1680, 'label': '105A8', 'order': 105, 'powers': [87, 58, 46, 37], 'representative': 128, 'size': 4}
  • id: 124366233
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 86, 'group_counter': 826, 'group_order': 1680, 'label': '105A-8', 'order': 105, 'powers': [88, 58, 46, 37], 'representative': 1552, 'size': 4}
  • id: 124366234
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 87, 'group_counter': 826, 'group_order': 1680, 'label': '105A16', 'order': 105, 'powers': [90, 59, 47, 36], 'representative': 256, 'size': 4}
  • id: 124366235
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 88, 'group_counter': 826, 'group_order': 1680, 'label': '105A-16', 'order': 105, 'powers': [89, 59, 47, 36], 'representative': 1424, 'size': 4}
  • id: 124366236
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 89, 'group_counter': 826, 'group_order': 1680, 'label': '105A17', 'order': 105, 'powers': [79, 56, 48, 37], 'representative': 272, 'size': 4}
  • id: 124366238
    {'aut_label': '105A1', 'centralizer': '4.d1.a1', 'counter': 90, 'group_counter': 826, 'group_order': 1680, 'label': '105A-17', 'order': 105, 'powers': [80, 56, 48, 37], 'representative': 1408, 'size': 4}
  • id: 124366239
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 91, 'group_counter': 826, 'group_order': 1680, 'label': '140A1', 'order': 140, 'powers': [67, 92, 49, 38], 'representative': 12, 'size': 4}
  • id: 124366240
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 92, 'group_counter': 826, 'group_order': 1680, 'label': '140A3', 'order': 140, 'powers': [68, 93, 50, 39], 'representative': 36, 'size': 4}
  • id: 124366241
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 93, 'group_counter': 826, 'group_order': 1680, 'label': '140A9', 'order': 140, 'powers': [69, 95, 51, 41], 'representative': 108, 'size': 4}
  • id: 124366242
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 94, 'group_counter': 826, 'group_order': 1680, 'label': '140A11', 'order': 140, 'powers': [70, 99, 50, 41], 'representative': 132, 'size': 4}
  • id: 124366243
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 95, 'group_counter': 826, 'group_order': 1680, 'label': '140A13', 'order': 140, 'powers': [71, 100, 49, 40], 'representative': 156, 'size': 4}
  • id: 124366244
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 96, 'group_counter': 826, 'group_order': 1680, 'label': '140A19', 'order': 140, 'powers': [69, 101, 51, 38], 'representative': 228, 'size': 4}
  • id: 124366245
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 97, 'group_counter': 826, 'group_order': 1680, 'label': '140A23', 'order': 140, 'powers': [72, 98, 51, 39], 'representative': 276, 'size': 4}
  • id: 124366246
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 98, 'group_counter': 826, 'group_order': 1680, 'label': '140A29', 'order': 140, 'powers': [67, 102, 49, 41], 'representative': 348, 'size': 4}
  • id: 124366247
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 99, 'group_counter': 826, 'group_order': 1680, 'label': '140A33', 'order': 140, 'powers': [72, 91, 51, 40], 'representative': 396, 'size': 4}
  • id: 124366112
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 100, 'group_counter': 826, 'group_order': 1680, 'label': '140A39', 'order': 140, 'powers': [70, 97, 50, 38], 'representative': 468, 'size': 4}
  • id: 124366113
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 101, 'group_counter': 826, 'group_order': 1680, 'label': '140A43', 'order': 140, 'powers': [71, 94, 49, 39], 'representative': 516, 'size': 4}
  • id: 124366114
    {'aut_label': '140A1', 'centralizer': '4.d1.a1', 'counter': 102, 'group_counter': 826, 'group_order': 1680, 'label': '140A53', 'order': 140, 'powers': [68, 96, 50, 40], 'representative': 636, 'size': 4}
  • id: 124366115
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 103, 'group_counter': 826, 'group_order': 1680, 'label': '210A1', 'order': 210, 'powers': [79, 67, 60, 52], 'representative': 8, 'size': 4}
  • id: 124366116
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 104, 'group_counter': 826, 'group_order': 1680, 'label': '210A-1', 'order': 210, 'powers': [80, 67, 60, 52], 'representative': 1672, 'size': 4}
  • id: 124366117
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 105, 'group_counter': 826, 'group_order': 1680, 'label': '210A11', 'order': 210, 'powers': [83, 70, 62, 52], 'representative': 88, 'size': 4}
  • id: 124366118
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 106, 'group_counter': 826, 'group_order': 1680, 'label': '210A-11', 'order': 210, 'powers': [84, 70, 62, 52], 'representative': 1592, 'size': 4}
  • id: 124366119
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 107, 'group_counter': 826, 'group_order': 1680, 'label': '210A13', 'order': 210, 'powers': [85, 71, 60, 53], 'representative': 104, 'size': 4}
  • id: 124366120
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 108, 'group_counter': 826, 'group_order': 1680, 'label': '210A-13', 'order': 210, 'powers': [86, 71, 60, 53], 'representative': 1576, 'size': 4}
  • id: 124366121
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 109, 'group_counter': 826, 'group_order': 1680, 'label': '210A17', 'order': 210, 'powers': [89, 68, 62, 53], 'representative': 136, 'size': 4}
  • id: 124366123
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 110, 'group_counter': 826, 'group_order': 1680, 'label': '210A-17', 'order': 210, 'powers': [90, 68, 62, 53], 'representative': 1544, 'size': 4}
  • id: 124366124
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 111, 'group_counter': 826, 'group_order': 1680, 'label': '210A19', 'order': 210, 'powers': [87, 69, 61, 52], 'representative': 152, 'size': 4}
  • id: 124366125
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 112, 'group_counter': 826, 'group_order': 1680, 'label': '210A-19', 'order': 210, 'powers': [88, 69, 61, 52], 'representative': 1528, 'size': 4}
  • id: 124366126
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 113, 'group_counter': 826, 'group_order': 1680, 'label': '210A23', 'order': 210, 'powers': [82, 72, 61, 53], 'representative': 184, 'size': 4}
  • id: 124366127
    {'aut_label': '210A1', 'centralizer': '4.d1.a1', 'counter': 114, 'group_counter': 826, 'group_order': 1680, 'label': '210A-23', 'order': 210, 'powers': [81, 72, 61, 53], 'representative': 1496, 'size': 4}
  • id: 124366128
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 115, 'group_counter': 826, 'group_order': 1680, 'label': '420A1', 'order': 420, 'powers': [103, 91, 73, 63], 'representative': 4, 'size': 4}
  • id: 124366129
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 116, 'group_counter': 826, 'group_order': 1680, 'label': '420A-1', 'order': 420, 'powers': [104, 91, 74, 63], 'representative': 724, 'size': 4}
  • id: 124366130
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 117, 'group_counter': 826, 'group_order': 1680, 'label': '420A11', 'order': 420, 'powers': [105, 94, 77, 65], 'representative': 44, 'size': 4}
  • id: 124366131
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 118, 'group_counter': 826, 'group_order': 1680, 'label': '420A-11', 'order': 420, 'powers': [106, 94, 78, 65], 'representative': 1636, 'size': 4}
  • id: 124366132
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 119, 'group_counter': 826, 'group_order': 1680, 'label': '420A13', 'order': 420, 'powers': [107, 95, 74, 64], 'representative': 52, 'size': 4}
  • id: 124366134
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 120, 'group_counter': 826, 'group_order': 1680, 'label': '420A-13', 'order': 420, 'powers': [108, 95, 73, 64], 'representative': 1012, 'size': 4}
  • id: 124366135
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 121, 'group_counter': 826, 'group_order': 1680, 'label': '420A17', 'order': 420, 'powers': [109, 92, 77, 66], 'representative': 68, 'size': 4}
  • id: 124366136
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 122, 'group_counter': 826, 'group_order': 1680, 'label': '420A-17', 'order': 420, 'powers': [110, 92, 78, 66], 'representative': 628, 'size': 4}
  • id: 124366137
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 123, 'group_counter': 826, 'group_order': 1680, 'label': '420A19', 'order': 420, 'powers': [111, 96, 75, 63], 'representative': 484, 'size': 4}
  • id: 124366138
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 124, 'group_counter': 826, 'group_order': 1680, 'label': '420A-19', 'order': 420, 'powers': [112, 96, 76, 63], 'representative': 244, 'size': 4}
  • id: 124366139
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 125, 'group_counter': 826, 'group_order': 1680, 'label': '420A23', 'order': 420, 'powers': [113, 97, 75, 66], 'representative': 148, 'size': 4}
  • id: 124366140
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 126, 'group_counter': 826, 'group_order': 1680, 'label': '420A-23', 'order': 420, 'powers': [114, 97, 76, 66], 'representative': 1588, 'size': 4}
  • id: 124366141
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 127, 'group_counter': 826, 'group_order': 1680, 'label': '420A29', 'order': 420, 'powers': [103, 98, 74, 65], 'representative': 116, 'size': 4}
  • id: 124366142
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 128, 'group_counter': 826, 'group_order': 1680, 'label': '420A-29', 'order': 420, 'powers': [104, 98, 73, 65], 'representative': 676, 'size': 4}
  • id: 124366143
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 129, 'group_counter': 826, 'group_order': 1680, 'label': '420A43', 'order': 420, 'powers': [108, 101, 74, 66], 'representative': 388, 'size': 4}
  • id: 124366145
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 130, 'group_counter': 826, 'group_order': 1680, 'label': '420A-43', 'order': 420, 'powers': [107, 101, 73, 66], 'representative': 1348, 'size': 4}
  • id: 124366146
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 131, 'group_counter': 826, 'group_order': 1680, 'label': '420A47', 'order': 420, 'powers': [113, 99, 76, 64], 'representative': 1252, 'size': 4}
  • id: 124366147
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 132, 'group_counter': 826, 'group_order': 1680, 'label': '420A-47', 'order': 420, 'powers': [114, 99, 75, 64], 'representative': 1492, 'size': 4}
  • id: 124366148
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 133, 'group_counter': 826, 'group_order': 1680, 'label': '420A53', 'order': 420, 'powers': [109, 102, 78, 64], 'representative': 292, 'size': 4}
  • id: 124366149
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 134, 'group_counter': 826, 'group_order': 1680, 'label': '420A-53', 'order': 420, 'powers': [110, 102, 77, 64], 'representative': 772, 'size': 4}
  • id: 124366150
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 135, 'group_counter': 826, 'group_order': 1680, 'label': '420A59', 'order': 420, 'powers': [105, 100, 78, 63], 'representative': 964, 'size': 4}
  • id: 124366151
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 136, 'group_counter': 826, 'group_order': 1680, 'label': '420A-59', 'order': 420, 'powers': [106, 100, 77, 63], 'representative': 1444, 'size': 4}
  • id: 124366152
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 137, 'group_counter': 826, 'group_order': 1680, 'label': '420A89', 'order': 420, 'powers': [112, 93, 75, 65], 'representative': 1156, 'size': 4}
  • id: 124366153
    {'aut_label': '420A1', 'centralizer': '4.d1.a1', 'counter': 138, 'group_counter': 826, 'group_order': 1680, 'label': '420A-89', 'order': 420, 'powers': [111, 93, 76, 65], 'representative': 916, 'size': 4}
• gps_qchar •

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

  
  
  • id: 7529389
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529400
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529411
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529421
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529422
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529423
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529424
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529425
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529426
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, 2, 2, -1, 2, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529390
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, -2, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, 2, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529391
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 2, -2, 0, 0, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529392
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, -2, -2, -1, 2, 0, 2, 2, -1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529393
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, -2, 2, -1, -2, 0, 2, 2, -1, 1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529394
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, 2, -2, -1, -2, 0, 2, 2, -1, -1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529395
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2g', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, -1, -1, 4, 0, 0, 4, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529396
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2h', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, -4, 4, -1, -1, 4, 0, 0, 4, 4, 4, -1, -1, 1, 1, 1, 1, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529397
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2i', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 4, -4, -1, -1, 4, 0, 0, 4, 4, 4, -1, -1, 1, 1, 1, 1, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529398
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2j', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, -4, -4, -1, -1, 4, 0, 0, 4, 4, 4, -1, -1, -1, -1, -1, -1, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529406
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 4, 2, 0, 0, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529399
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2k', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, 6, 0, 0, 6, 6, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 0, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529401
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2l', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -6, -6, 0, 0, 6, 6, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 0, 6, -1, -1, -1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529402
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2m', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -6, 6, 0, 0, 6, -6, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 0, -6, -1, -1, -1, 1, 1, 1, -1, -1, -1, 6, 6, -6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529403
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 6, -6, 0, 0, 6, -6, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, 0, 0, 0, 0, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 6, 6, -6, -6, -6, -6, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529404
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2o', 'multiplicity': 4, 'nt': [20, 10], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -2, -2, -8, 0, 0, 8, 8, 8, 2, 2, 2, -2, 2, -2, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, -8, -8, -8, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529405
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.2p', 'multiplicity': 4, 'nt': [20, 10], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, 0, 0, -2, -2, -8, 0, 0, 8, 8, 8, 2, 2, -2, 2, -2, 2, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, -8, -8, -8, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529407
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4b', 'multiplicity': 2, 'nt': [15, 7], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -4, 8, 0, -2, -2, -4, 0, 0, 8, 8, 8, -2, -2, 0, 0, 0, 0, -4, 8, 8, 8, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -4, -4, -4, 8, 8, 8, 1, 1, -2, -2, -2, -2, -2, -2, -4, -4, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529408
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4c', 'multiplicity': 2, 'nt': [30, 21], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -4, -8, 0, -2, -2, -4, 0, 0, 8, 8, 8, -2, -2, 0, 0, 0, 0, 4, 8, 8, 8, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -4, -4, -4, -8, -8, -8, 1, 1, -2, -2, -2, -2, -2, -2, -4, -4, -4, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529409
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4d', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, 0, -6, 12, 0, 12, 12, -6, 0, 0, -2, -2, -2, 12, 12, 0, 0, 0, 0, -6, -2, -2, -2, 0, 0, 0, 0, 0, 0, -6, -6, 12, 12, 12, 12, 0, 0, 0, 0, 1, 1, 1, -2, -2, -2, -6, -6, -2, -2, -2, -2, -2, -2, 1, 1, 1, -6, -6, -6, -6, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529410
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4e', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 12, 12, -12, 0, 0, -2, -2, -2, -12, -12, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, -12, -12, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529412
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4f', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, 0, -6, -12, 0, 12, 12, -6, 0, 0, -2, -2, -2, 12, 12, 0, 0, 0, 0, 6, -2, -2, -2, 0, 0, 0, 0, 0, 0, -6, -6, -12, -12, -12, -12, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, -6, -6, -2, -2, -2, -2, -2, -2, 1, 1, 1, 6, 6, 6, 6, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529413
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4g', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, -8, 0, 0, -4, -4, 8, 0, 0, 16, 16, 16, 4, 4, 0, 0, 0, 0, 0, -16, -16, -16, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, -2, -2, -4, -4, -4, -4, -4, -4, 8, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529414
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4h', 'multiplicity': 6, 'nt': [35, 7], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, 0, 0, 24, 24, 0, -6, -6, 24, 0, 0, -4, -4, -4, -6, -6, 0, 0, 0, 0, 24, -4, -4, -4, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -6, -6, 1, 1, 1, 1, 1, 1, -4, -4, -4, -6, -6, -6, -6, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 7529415
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4i', 'multiplicity': 6, 'nt': [70, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, 0, 0, 24, -24, 0, -6, -6, 24, 0, 0, -4, -4, -4, -6, -6, 0, 0, 0, 0, -24, -4, -4, -4, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, 0, 0, 0, 0, -4, -4, -4, 4, 4, 4, -6, -6, 1, 1, 1, 1, 1, 1, -4, -4, -4, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 7529416
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4j', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, 0, -12, 0, 0, 24, 24, 12, 0, 0, -4, -4, -4, -24, -24, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 12, 12, -4, -4, -4, -4, -4, -4, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529417
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4k', 'multiplicity': 12, 'nt': [105, 0], 'qdim': 48, 'qvalues': [48, 48, 0, 0, 0, 0, 0, 0, -24, 48, 0, -12, -12, -24, 0, 0, -8, -8, -8, -12, -12, 0, 0, 0, 0, -24, -8, -8, -8, 0, 0, 0, 0, 0, 0, 6, 6, -12, -12, -12, -12, 0, 0, 0, 0, 4, 4, 4, -8, -8, -8, 6, 6, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 7529418
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4l', 'multiplicity': 12, 'nt': [140, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 48, 0, 0, -12, -12, -48, 0, 0, -8, -8, -8, 12, 12, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 12, 12, 2, 2, 2, 2, 2, 2, 8, 8, 8, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7529419
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4m', 'multiplicity': 12, 'nt': [210, 0], 'qdim': 48, 'qvalues': [48, 48, 0, 0, 0, 0, 0, 0, -24, -48, 0, -12, -12, -24, 0, 0, -8, -8, -8, -12, -12, 0, 0, 0, 0, 24, -8, -8, -8, 0, 0, 0, 0, 0, 0, 6, 6, 12, 12, 12, 12, 0, 0, 0, 0, 4, 4, 4, 8, 8, 8, 6, 6, 2, 2, 2, 2, 2, 2, 4, 4, 4, -6, -6, -6, -6, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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: 7529420
    {'cdim': 4, 'counter': 38, 'faithful': True, 'group': '1680.826', 'group_order': 1680, 'image': None, 'label': '1680.826.4n', 'multiplicity': 24, 'nt': [420, 0], 'qdim': 96, 'qvalues': [96, -96, 0, 0, 0, 0, 0, 0, -48, 0, 0, -24, -24, 48, 0, 0, -16, -16, -16, 24, 24, 0, 0, 0, 0, 0, 16, 16, 16, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, -12, -12, 4, 4, 4, 4, 4, 4, -8, -8, -8, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 17830069
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1680, 'label': '1680.826.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830119
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 840, 'label': '1680.826.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830130
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 840, 'label': '1680.826.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830141
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 840, 'label': '1680.826.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830152
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 840, 'label': '1680.826.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830163
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 840, 'label': '1680.826.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830174
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 840, 'label': '1680.826.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830185
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1680, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 840, 'label': '1680.826.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830196
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 280, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 280, 'label': '1680.826.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830070
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 420, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 210, 'label': '1680.826.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830081
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 420, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 210, 'label': '1680.826.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830092
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 280, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 140, 'label': '1680.826.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 17830103
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 280, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 140, 'label': '1680.826.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830113
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 280, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 140, 'label': '1680.826.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 17830114
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 15, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 168, 'label': '1680.826.2g1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830115
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 16, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 168, 'label': '1680.826.2g2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830116
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 17, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.c1.a1', 'kernel_order': 84, 'label': '1680.826.2h1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830117
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 18, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.c1.a1', 'kernel_order': 84, 'label': '1680.826.2h2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830118
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 19, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.b1.a1', 'kernel_order': 84, 'label': '1680.826.2i1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830120
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 20, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.b1.a1', 'kernel_order': 84, 'label': '1680.826.2i2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830121
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 21, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 84, 'label': '1680.826.2j1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830122
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 168, 'counter': 22, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 84, 'label': '1680.826.2j2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830123
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 23, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 120, 'label': '1680.826.2k1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830124
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 24, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 120, 'label': '1680.826.2k2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830125
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 120, 'label': '1680.826.2k3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830126
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 60, 'label': '1680.826.2l1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830127
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 27, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 60, 'label': '1680.826.2l2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830128
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 28, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 60, 'label': '1680.826.2l3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830129
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 29, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 60, 'label': '1680.826.2m1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830131
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 30, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 60, 'label': '1680.826.2m2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830132
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 31, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 60, 'label': '1680.826.2m3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830133
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 32, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 60, 'label': '1680.826.2n1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830134
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 33, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 60, 'label': '1680.826.2n2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830135
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 120, 'counter': 34, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 60, 'label': '1680.826.2n3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830136
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 35, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.b1', 'kernel_order': 42, 'label': '1680.826.2o1', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830137
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 36, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.b1', 'kernel_order': 42, 'label': '1680.826.2o2', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830138
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 37, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.b1', 'kernel_order': 42, 'label': '1680.826.2o3', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830139
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 38, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.b1', 'kernel_order': 42, 'label': '1680.826.2o4', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830140
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 39, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 42, 'label': '1680.826.2p1', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830142
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 40, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 42, 'label': '1680.826.2p2', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830143
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 41, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 42, 'label': '1680.826.2p3', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830144
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 84, 'counter': 42, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '40.6', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 42, 'label': '1680.826.2p4', 'nt': [20, 10], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830145
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 70, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 35, 'label': '1680.826.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830146
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 28, 'counter': 44, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 28, 'label': '1680.826.4b1', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830147
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 28, 'counter': 45, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 28, 'label': '1680.826.4b2', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830148
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 28, 'counter': 46, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '120.42', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 14, 'label': '1680.826.4c1', 'nt': [30, 21], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830149
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 28, 'counter': 47, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '120.42', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 14, 'label': '1680.826.4c2', 'nt': [30, 21], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830150
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 48, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 20, 'label': '1680.826.4d1', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 17830151
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 49, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 20, 'label': '1680.826.4d2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830153
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 50, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 20, 'label': '1680.826.4d3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830154
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 30, 'counter': 51, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 15, 'label': '1680.826.4e1', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 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]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830155
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 30, 'counter': 52, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 15, 'label': '1680.826.4e2', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 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]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830156
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 30, 'counter': 53, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 15, 'label': '1680.826.4e3', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 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]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17830157
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 54, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 10, 'label': '1680.826.4f1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 17830158
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 55, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 10, 'label': '1680.826.4f2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830159
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 20, 'counter': 56, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 10, 'label': '1680.826.4f3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830160
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 14, 'counter': 57, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '240.137', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 7, 'label': '1680.826.4g1', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 17830161
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 14, 'counter': 58, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '240.137', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 7, 'label': '1680.826.4g2', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 17830162
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 14, 'counter': 59, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '240.137', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 7, 'label': '1680.826.4g3', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]]]}
  • id: 17830164
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 14, 'counter': 60, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '240.137', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 7, 'label': '1680.826.4g4', 'nt': [60, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 17830165
    {'center': '140.a1.a1', 'center_index': 140, 'center_order': 12, 'counter': 61, 'cyclotomic_n': 35, 'dim': 4, 'faithful': False, 'field': [-1, -2, 7, 2, -7, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '140.7', 'image_order': 140, 'indicator': 1, 'kernel': '140.a1.a1', 'kernel_order': 12, 'label': '1680.826.4h1', 'nt': [35, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 15], [2, -15]], [[2, 5], [2, -5]], [[2, 10], [2, -10]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 10], [2, -10]], [[2, 5], [2, -5]], [[2, 15], [2, -15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], 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  • id: 17830166
    {'center': '140.a1.a1', 'center_index': 140, 'center_order': 12, 'counter': 62, 'cyclotomic_n': 35, 'dim': 4, 'faithful': False, 'field': [-1, -2, 7, 2, -7, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '140.7', 'image_order': 140, 'indicator': 1, 'kernel': '140.a1.a1', 'kernel_order': 12, 'label': '1680.826.4h2', 'nt': [35, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 15], [2, -15]], [[2, 5], [2, -5]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 5], [2, -5]], [[2, 15], [2, -15]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], 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  • id: 17830167
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  • id: 17830169
    {'center': '140.a1.a1', 'center_index': 140, 'center_order': 12, 'counter': 65, 'cyclotomic_n': 35, 'dim': 4, 'faithful': False, 'field': [-1, -2, 7, 2, -7, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '140.7', 'image_order': 140, 'indicator': 1, 'kernel': '140.a1.a1', 'kernel_order': 12, 'label': '1680.826.4h5', 'nt': [35, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 15], [2, -15]], [[2, 5], [2, -5]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 5], [2, -5]], [[2, 15], [2, -15]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], 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  • id: 17830170
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  • id: 17830172
    {'center': '140.a1.a1', 'center_index': 140, 'center_order': 12, 'counter': 68, 'cyclotomic_n': 35, 'dim': 4, 'faithful': False, 'field': [-1, -2, 7, 2, -7, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '280.36', 'image_order': 280, 'indicator': 1, 'kernel': '280.a1.a1', 'kernel_order': 6, 'label': '1680.826.4i2', 'nt': [70, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 15], [2, -15]], [[2, 5], [2, -5]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 5], [2, -5]], [[2, 15], [2, -15]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[-2, 14], [-2, -14]], [[-2, 7], [-2, -7]], [[-2, 7], [-2, -7]], [[-2, 14], [-2, 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  • id: 17830173
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  • id: 17830175
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  • id: 17830176
    {'center': '140.a1.a1', 'center_index': 140, 'center_order': 12, 'counter': 71, 'cyclotomic_n': 35, 'dim': 4, 'faithful': False, 'field': [-1, -2, 7, 2, -7, -1, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '280.36', 'image_order': 280, 'indicator': 1, 'kernel': '280.a1.a1', 'kernel_order': 6, 'label': '1680.826.4i5', 'nt': [70, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 7], [2, -7]], [[2, 14], [2, -14]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 15], [2, -15]], [[2, 5], [2, -5]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 5], [2, -5]], [[2, 15], [2, -15]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 14], [2, -14]], [[2, 7], [2, -7]], [[-2, 7], [-2, -7]], [[-2, 14], [-2, -14]], [[-2, 14], [-2, -14]], [[-2, 7], 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  • id: 17830177
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  • id: 17830178
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  • id: 17830179
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 10, 'counter': 74, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 5, 'label': '1680.826.4j2', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]]]}
  • id: 17830180
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  • id: 17830181
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 10, 'counter': 76, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 5, 'label': '1680.826.4j4', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 18], [2, -18]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]]]}
  • id: 17830182
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  • id: 17830183
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  • id: 17830184
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  • id: 17830194
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  • id: 17830195
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  • id: 17830197
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  • id: 17830186
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  • id: 17830187
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  • id: 17830188
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  • id: 17830189
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  • id: 17830190
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  • id: 17830191
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  • id: 17830192
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  • id: 17830193
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  • id: 17830198
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 91, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l1', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[-2, 28], [-2, -28]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-2, 21], [-2, -21]], 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  • id: 17830071
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 100, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l10', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[2, 14], [2, -14]], [[-2, 28], [-2, -28]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[2, 7], [2, -7]], 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  • id: 17830072
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 101, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l11', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[2, 14], [2, -14]], [[-2, 28], [-2, -28]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-2, 7], [-2, -7]], 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  • id: 17830073
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 102, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l12', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[2, 14], [2, -14]], [[-2, 28], [-2, -28]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[2, 7], [2, -7]], 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  • id: 17830199
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 92, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l2', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[-2, 28], [-2, -28]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[2, 21], [2, -21]], 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  • id: 17830200
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 93, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l3', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[-2, 28], [-2, -28]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-2, 21], [-2, -21]], 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  • id: 17830201
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  • id: 17830202
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  • id: 17830203
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 96, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l6', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[-2, 28], [-2, -28]], [[2, 14], [2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[2, 21], [2, -21]], 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  • id: 17830204
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 97, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l7', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[-2, 30], [-2, -30]], [[2, 14], [2, -14]], [[-2, 28], [-2, -28]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 30], [2, -30]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-2, 7], [-2, -7]], 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  • id: 17830205
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  • id: 17830206
    {'center': '280.a1.a1', 'center_index': 280, 'center_order': 6, 'counter': 99, 'cyclotomic_n': 140, 'dim': 4, 'faithful': False, 'field': [1, 22, 90, -324, -175, 734, -23, -412, 74, 74, -17, -4, 1], 'group': '1680.826', 'group_counter': 826, 'group_order': 1680, 'image': None, 'image_isoclass': '560.120', 'image_order': 560, 'indicator': 1, 'kernel': '560.a1.a1', 'kernel_order': 3, 'label': '1680.826.4l9', 'nt': [140, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 28], [2, -28]], [[-2, 14], [-2, -14]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 30], [-2, -30]], [[-2, 10], [-2, -10]], [[2, 20], [2, -20]], [[2, 14], [2, -14]], [[-2, 28], [-2, -28]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 20], [-2, -20]], [[2, 10], [2, -10]], [[2, 30], [2, -30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 14], [-2, -14]], [[2, 28], [2, -28]], [[-2, 7], [-2, -7]], 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  • id: 17830074
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  • id: 17830084
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  • id: 17830085
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  • id: 17830086
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  • id: 17830075
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  • id: 17830076
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  • id: 17830077
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  • id: 17830078
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  • id: 17830079
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  • id: 17830080
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  • id: 17830082
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  • id: 17830083
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  • id: 17830087
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  • id: 17830097
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  • id: 17830098
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  • id: 17830099
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  • id: 17830100
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  • id: 17830101
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  • id: 17830102
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  • id: 17830104
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  • id: 17830105
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  • id: 17830106
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  • id: 17830107
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  • id: 17830088
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  • id: 17830108
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  • id: 17830109
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  • id: 17830110
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  • id: 17830111
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  • id: 17830112
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  • id: 17830089
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  • id: 17830090
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  • id: 17830091
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  • id: 17830093
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  • id: 17830094
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  • id: 17830095
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  • id: 17830096
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82], [1, 90], [-1, 92], [1, 94]], [[1, 2], [1, 6], [1, 10], [1, 12], [1, 16], [1, 20], [-1, 32], [-1, 36], [-1, 38], [-1, 40], [-1, 42], [-1, 44], [-1, 48], [-1, 50], [-1, 52], [-1, 54], [-1, 58], [1, 70], [2, 74], [1, 78], [1, 80], [1, 84], [1, 88], [2, 94]], [[1, 0], [-2, 2], [1, 10], [1, 14], [1, 18], [1, 24], [1, 28], [1, 32], [-1, 48], [-1, 52], [-1, 56], [-1, 58], [-1, 62], [-1, 66], [1, 68], [-1, 70], [1, 72], [1, 78], [-1, 80], [1, 92]], [[-1, 0], [1, 2], [-1, 10], [1, 12], [-1, 14], [1, 16], [-1, 18], [1, 20], [-1, 24], [1, 26], [1, 30], [1, 34], [-1, 38], [-1, 46], [-1, 50], [1, 52], [-1, 54], [-1, 58], [-1, 60], [-1, 64], [1, 66], [-1, 68], [1, 70], [-1, 72], [2, 80], [-1, 82], [1, 84], [2, 88], [1, 94]], [[2, 0], [2, 6], [1, 8], [2, 10], [-2, 12], [2, 14], [1, 20], [-2, 22], [2, 24], [-2, 26], [-2, 30], [-1, 34], [-2, 36], [-2, 40], [-2, 44], [-1, 48], [2, 60], [-2, 62], [2, 64], [2, 68], [2, 74], [-1, 76], [1, 78], [-2, 80], [2, 82], [-1, 90], [1, 92], [-2, 94]], [[-1, 0], [1, 2], [-2, 4], [-2, 8], [-1, 10], [-1, 12], [-3, 14], [1, 16], [-3, 18], [-2, 22], [-1, 24], [-2, 26], [-1, 28], [1, 30], [-1, 32], [2, 34], [2, 38], [1, 40], [2, 42], [3, 44], [2, 46], [3, 48], [2, 50], [3, 52], [1, 54], [3, 56], [2, 60], [1, 62], [1, 66], [-1, 68], [1, 70], [-3, 72], [-2, 76], [-1, 78], [-1, 80], [-2, 82], [-2, 86], [-2, 90], [-1, 92]], [[2, 0], [2, 4], [-1, 6], [1, 8], [2, 10], [2, 14], [2, 18], [-2, 30], [-1, 34], [-1, 36], [-2, 38], [-2, 40], [-2, 42], [-2, 44], [-2, 46], [-2, 48], [-1, 50], [-2, 52], [-2, 56], [2, 64], [2, 68], [2, 72], [3, 76], [2, 78], [2, 82], [2, 86], [1, 92]], [[1, 2], [1, 58], [-1, 68], [1, 82]], [[1, 4], [1, 8], [1, 12], [1, 14], [-1, 16], [1, 18], [1, 22], [2, 26], [-1, 34], [-1, 38], [-1, 42], [-2, 44], [-1, 46], [-1, 48], [-1, 50], [-1, 52], [-1, 54], [-1, 56], [-1, 60], [1, 72], [1, 76], [1, 80], [1, 86], [1, 90]], [[-2, 0], [-1, 4], [-2, 10], [1, 12], [-2, 14], [-1, 18], [1, 22], [-1, 24], [1, 26], [2, 30], [1, 34], [2, 36], [1, 38], [2, 40], [1, 42], [2, 44], [1, 46], [1, 48], [1, 52], [1, 56], [-1, 60], [-3, 64], [-2, 68], [-1, 72], [-1, 74], [-2, 76], [-2, 78], [1, 80], [-2, 82], [-1, 86], [1, 90], [-1, 92], [1, 94]], [[1, 0], [-2, 2], [-1, 6], [-1, 10], [-2, 12], [1, 14], [-2, 16], [1, 18], [-2, 20], [1, 24], [-1, 26], [-1, 30], [2, 32], [-1, 34], [1, 36], [1, 38], [1, 40], [1, 42], [1, 44], [1, 46], [1, 48], [2, 50], [1, 52], [2, 54], [2, 58], [1, 64], [-1, 66], [1, 68], [-2, 70], [1, 72], [-2, 74], [-1, 78], [-2, 80], [1, 82], [-2, 84], [-2, 88], [-3, 94]], [[-1, 32], [1, 38], [-1, 52], [-1, 88]], [[-2, 1], [1, 3], [-1, 5], [-1, 7], [-2, 11], [2, 13], [-3, 15], [-1, 19], [-1, 21], [-2, 25], [1, 27], [-2, 29], [1, 31], [-1, 33], [1, 35], [1, 37], [2, 41], [1, 43], [2, 45], [1, 47], [2, 49], [1, 51], [2, 53], [2, 57], [1, 59], [2, 63], [-1, 65], [1, 67], [-2, 69], [2, 71], [-1, 73], [-1, 75], [-2, 79], [1, 81], [-3, 83], [-1, 87], [-1, 89], [-2, 93], [1, 95]], [[-1, 3], [-2, 7], [-2, 11], [-2, 13], [-1, 17], [-2, 21], [-1, 25], [2, 33], [2, 37], [1, 39], [2, 41], [2, 43], [2, 45], [2, 47], [2, 49], [2, 51], [1, 53], [2, 55], [2, 59], [-1, 67], [-2, 71], [-1, 73], [-2, 75], [-2, 79], [-1, 81], [-2, 85], [-1, 87], [-2, 89], [-1, 95]], [[1, 3], [2, 7], [2, 11], [2, 13], [1, 17], [2, 21], [1, 25], [-2, 33], [-2, 37], [-1, 39], [-2, 41], [-2, 43], [-2, 45], [-2, 47], [-2, 49], [-2, 51], [-1, 53], [-2, 55], [-2, 59], [1, 67], [2, 71], [1, 73], [2, 75], [2, 79], [1, 81], [2, 85], [1, 87], [2, 89], [1, 95]], [[1, 1], [-1, 3], [-1, 13], [1, 15], [-1, 17], [-1, 21], [1, 23], [-1, 27], [-1, 31], [1, 33], [-1, 35], [1, 37], [1, 51], [1, 55], [1, 59], [1, 61], [1, 65], [1, 69], [-1, 71], [1, 73], [-1, 81], [1, 83], [-1, 85], [-1, 89], [-1, 95]], [[-1, 3], [-1, 9], [1, 11], [-2, 13], [1, 15], [-1, 17], [-1, 23], [1, 25], [-1, 27], [2, 29], [-1, 31], [1, 33], [1, 39], [-1, 41], [1, 43], [1, 47], [1, 51], [1, 55], [1, 61], [-1, 63], [1, 65], [-1, 67], [-1, 71], [-1, 77], [1, 79], [-2, 81], [1, 83], [-1, 85], [-1, 91], [1, 93], [-1, 95]], [[1, 17], [-1, 53], [-1, 67], [-1, 73]], [[-1, 1], [-1, 11], [-1, 15], [-1, 23], [1, 31], [1, 33], [1, 35], [1, 39], [1, 41], [1, 43], [1, 45], [1, 47], [1, 49], [1, 53], [1, 57], [-1, 61], [-1, 65], [-1, 69], [-1, 73], [-1, 75], [-1, 77], [-1, 79], [-1, 83], [-1, 87], [1, 93]], [[1, 1], [-1, 3], [1, 5], [1, 11], [-2, 13], [3, 15], [-1, 17], [1, 19], [1, 25], [2, 29], [-1, 31], [1, 33], [-1, 35], [-1, 41], [-1, 45], [-1, 49], [-1, 53], [-2, 57], [-1, 63], [1, 65], [-1, 67], [1, 69], [-2, 71], [1, 73], [1, 79], [-1, 81], [2, 83], [-2, 85], [1, 87], [1, 93], [-1, 95]], [[-1, 7], [2, 9], [-1, 11], [1, 13], [1, 17], [2, 19], [-1, 21], [2, 23], [2, 27], [1, 31], [1, 33], [1, 37], [-1, 39], [1, 41], [-1, 43], [-1, 47], [-1, 49], [-1, 51], [-2, 53], [-1, 55], [-2, 57], [-2, 61], [-2, 65], [-1, 67], [-1, 71], [-1, 75], [2, 77], [-1, 79], [2, 81], [1, 85], [1, 87], [-1, 89], [2, 91], [2, 95]], [[2, 1], [-1, 3], [1, 5], [1, 7], [2, 11], [-2, 13], [3, 15], [1, 19], [1, 21], [2, 25], [-1, 27], [2, 29], [-1, 31], [1, 33], [-1, 35], [-1, 37], [-2, 41], [-1, 43], [-2, 45], [-1, 47], [-2, 49], [-1, 51], [-2, 53], [-2, 57], [-1, 59], [-2, 63], [1, 65], [-1, 67], [2, 69], [-2, 71], [1, 73], [1, 75], [2, 79], [-1, 81], [3, 83], [1, 87], [1, 89], [2, 93], [-1, 95]], [[1, 3], [1, 9], [-1, 11], [2, 13], [-1, 15], [1, 17], [1, 23], [-1, 25], [1, 27], [-2, 29], [1, 31], [-1, 33], [-1, 39], [1, 41], [-1, 43], [-1, 47], [-1, 51], [-1, 55], [-1, 61], [1, 63], [-1, 65], [1, 67], [1, 71], [1, 77], [-1, 79], [2, 81], [-1, 83], [1, 85], [1, 91], [-1, 93], [1, 95]], [[1, 3], [1, 7], [1, 11], [1, 13], [1, 17], [1, 21], [1, 31], [-1, 33], [-1, 37], [-1, 41], [-1, 43], [-1, 45], [-1, 47], [-1, 49], [-1, 51], [-1, 55], [-2, 59], [1, 67], [1, 71], [1, 75], [1, 79], [1, 81], [1, 85], [1, 89]], [[1, 1], [-1, 3], [1, 5], [1, 7], [2, 11], [-1, 13], [3, 15], [1, 19], [1, 21], [2, 25], [-1, 27], [2, 29], [-1, 31], [1, 33], [-1, 35], [-1, 37], [-2, 41], [-1, 43], [-2, 45], [-1, 47], [-2, 49], [-1, 51], [-2, 53], [-1, 55], [-1, 57], [-1, 59], [-2, 63], [1, 65], [-1, 67], [1, 69], [-1, 71], [1, 73], [1, 75], [2, 79], [-1, 81], [2, 83], [-1, 85], [1, 87], [1, 89], [2, 93], [-1, 95]], [[-1, 17], [1, 53], [1, 67], [1, 73]], [[1, 1], [1, 5], [1, 9], [1, 11], [1, 15], [1, 19], [1, 23], [-1, 31], [-1, 35], [-1, 39], [-1, 41], [-1, 43], [-1, 45], [-1, 47], [-1, 49], [-1, 53], [-1, 57], [1, 61], [1, 69], [1, 73], [1, 77], [1, 79], [1, 83], [1, 87], [-1, 89]], [[-1, 3], [-1, 7], [-1, 11], [-1, 13], [-1, 17], [-1, 21], [-1, 31], [1, 33], [1, 37], [1, 41], [1, 43], [1, 45], [1, 47], [1, 49], [1, 51], [1, 55], [2, 59], [-1, 67], [-1, 71], [-1, 75], [-1, 79], [-1, 81], [-1, 85], [-1, 89]], [[1, 1], [1, 11], [1, 15], [1, 23], [-1, 31], [-1, 33], [-1, 35], [-1, 39], [-1, 41], [-1, 43], [-1, 45], [-1, 47], [-1, 49], [-1, 53], [-1, 57], [1, 61], [1, 65], [1, 69], [1, 73], [1, 75], [1, 77], [1, 79], [1, 83], [1, 87], [-1, 93]], [[-1, 1], [-1, 5], [-1, 9], [-1, 11], [-1, 15], [-1, 19], [-1, 23], [1, 31], [1, 35], [1, 39], [1, 41], [1, 43], [1, 45], [1, 47], [1, 49], [1, 53], [1, 57], [-1, 61], [-1, 69], [-1, 73], [-1, 77], [-1, 79], [-1, 83], [-1, 87], [1, 89]], [[-1, 1], [1, 3], [-1, 5], [-1, 11], [2, 13], [-3, 15], [1, 17], [-1, 19], [-1, 25], [-2, 29], [1, 31], [-1, 33], [1, 35], [1, 41], [1, 45], [1, 49], [1, 53], [2, 57], [1, 63], [-1, 65], [1, 67], [-1, 69], [2, 71], [-1, 73], [-1, 79], [1, 81], [-2, 83], [2, 85], [-1, 87], [-1, 93], [1, 95]], [[1, 7], [-2, 9], [1, 11], [-1, 13], [-1, 17], [-2, 19], [1, 21], [-2, 23], [-2, 27], [-1, 31], [-1, 33], [-1, 37], [1, 39], [-1, 41], [1, 43], [1, 47], [1, 49], [1, 51], [2, 53], [1, 55], [2, 57], [2, 61], [2, 65], [1, 67], [1, 71], [1, 75], [-2, 77], [1, 79], [-2, 81], [-1, 85], [-1, 87], [1, 89], [-2, 91], [-2, 95]], [[-1, 1], [1, 3], [1, 13], [-1, 15], [1, 17], [1, 21], [-1, 23], [1, 27], [1, 31], [-1, 33], [1, 35], [-1, 37], [-1, 51], [-1, 55], [-1, 59], [-1, 61], [-1, 65], [-1, 69], [1, 71], [-1, 73], [1, 81], [-1, 83], [1, 85], [1, 89], [1, 95]], [[-1, 1], [1, 3], [-1, 5], [-1, 7], [-2, 11], [1, 13], [-3, 15], [-1, 19], [-1, 21], [-2, 25], [1, 27], [-2, 29], [1, 31], [-1, 33], [1, 35], [1, 37], [2, 41], [1, 43], [2, 45], [1, 47], [2, 49], [1, 51], [2, 53], [1, 55], [1, 57], [1, 59], [2, 63], [-1, 65], [1, 67], [-1, 69], [1, 71], [-1, 73], [-1, 75], [-2, 79], [1, 81], [-2, 83], [1, 85], [-1, 87], [-1, 89], [-2, 93], [1, 95]], [[2, 1], [-1, 3], [2, 5], [1, 11], [-1, 13], [2, 15], [-1, 17], [-1, 21], [1, 23], [-1, 27], [-2, 31], [-2, 35], [-1, 39], [-1, 41], [-1, 43], [-1, 45], [-1, 47], [-1, 49], [-1, 53], [1, 55], [-1, 57], [1, 59], [1, 61], [1, 65], [2, 69], [-1, 71], [2, 73], [1, 77], [1, 79], [-1, 81], [2, 83], [-1, 85], [1, 87], [-1, 95]], [[-2, 1], [1, 3], [-2, 5], [-1, 11], [1, 13], [-2, 15], [1, 17], [1, 21], [-1, 23], [1, 27], [2, 31], [2, 35], [1, 39], [1, 41], [1, 43], [1, 45], [1, 47], [1, 49], [1, 53], [-1, 55], [1, 57], [-1, 59], [-1, 61], [-1, 65], [-2, 69], [1, 71], [-2, 73], [-1, 77], [-1, 79], [1, 81], [-2, 83], [1, 85], [-1, 87], [1, 95]]]}
• 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: 79904486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1680, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 210, 'label': '1680.826.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1680.826', 'subgroup_hash': 826, 'subgroup_order': 1680, 'subgroup_tex': 'C_{140}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 840, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.175', 'subgroup_hash': 175, 'subgroup_order': 840, 'subgroup_tex': 'C_{30}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 840, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.175', 'subgroup_hash': 175, 'subgroup_order': 840, 'subgroup_tex': 'C_{30}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 840, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.117', 'subgroup_hash': 117, 'subgroup_order': 840, 'subgroup_tex': 'C_{20}\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 840, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.89', 'subgroup_hash': 89, 'subgroup_order': 840, 'subgroup_tex': 'C_{21}:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 840, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.89', 'subgroup_hash': 89, 'subgroup_order': 840, 'subgroup_tex': 'C_{21}:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 840, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.123', 'subgroup_hash': 123, 'subgroup_order': 840, 'subgroup_tex': 'C_7\\times D_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 79904680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 840, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '840.108', 'subgroup_hash': 108, 'subgroup_order': 840, 'subgroup_tex': 'C_3\\times D_{140}', 'supersolvable': True, 'sylow': 0}
  • id: 79904691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 280, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 70, 'label': '1680.826.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '560.120', 'subgroup_hash': 120, 'subgroup_order': 560, 'subgroup_tex': 'D_7\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 420, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '420.38', 'subgroup_hash': 38, 'subgroup_order': 420, 'subgroup_tex': 'C_5\\times D_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 79904498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 420, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.39', 'subgroup_hash': 39, 'subgroup_order': 420, 'subgroup_tex': 'C_7\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 79904509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 420, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.39', 'subgroup_hash': 39, 'subgroup_order': 420, 'subgroup_tex': 'C_7\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 79904520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 420, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.36', 'subgroup_hash': 36, 'subgroup_order': 420, 'subgroup_tex': 'C_3\\times D_{70}', 'supersolvable': True, 'sylow': 0}
  • id: 79904531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 420, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.36', 'subgroup_hash': 36, 'subgroup_order': 420, 'subgroup_tex': 'C_3\\times D_{70}', 'supersolvable': True, 'sylow': 0}
  • id: 79904542
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 420, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.12', 'subgroup_hash': 12, 'subgroup_order': 420, 'subgroup_tex': 'C_{420}', 'supersolvable': True, 'sylow': 0}
  • id: 79904553
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 420, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '420.9', 'subgroup_hash': 9, 'subgroup_order': 420, 'subgroup_tex': 'C_{105}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 210, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '420.30', 'subgroup_hash': 30, 'subgroup_order': 420, 'subgroup_tex': 'C_{15}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 210, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '420.30', 'subgroup_hash': 30, 'subgroup_order': 420, 'subgroup_tex': 'C_{15}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 210, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.4.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '420.30', 'subgroup_hash': 30, 'subgroup_order': 420, 'subgroup_tex': 'C_{15}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 210, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.4.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '420.30', 'subgroup_hash': 30, 'subgroup_order': 420, 'subgroup_tex': 'C_{15}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 42, 'label': '1680.826.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.150', 'subgroup_hash': 150, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 280, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '280.26', 'subgroup_hash': 26, 'subgroup_order': 280, 'subgroup_tex': 'D_{140}', 'supersolvable': True, 'sylow': 0}
  • id: 79904618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 140, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.36', 'subgroup_hash': 36, 'subgroup_order': 280, 'subgroup_tex': 'D_5\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 140, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.36', 'subgroup_hash': 36, 'subgroup_order': 280, 'subgroup_tex': 'D_5\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 140, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.15', 'subgroup_hash': 15, 'subgroup_order': 280, 'subgroup_tex': 'D_7\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 140, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.12', 'subgroup_hash': 12, 'subgroup_order': 280, 'subgroup_tex': 'C_7:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 140, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.12', 'subgroup_hash': 12, 'subgroup_order': 280, 'subgroup_tex': 'C_7:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 140, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '280.21', 'subgroup_hash': 21, 'subgroup_order': 280, 'subgroup_tex': 'C_7\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '1680.826.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, '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': '240.137', 'subgroup_hash': 137, 'subgroup_order': 240, 'subgroup_tex': 'S_3\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904626
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 210, 'counter': 30, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '210.12', 'subgroup_hash': 12, 'subgroup_order': 210, 'subgroup_tex': 'C_{210}', 'supersolvable': True, 'sylow': 0}
  • id: 79904627
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 210, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '210.9', 'subgroup_hash': 9, 'subgroup_order': 210, 'subgroup_tex': 'C_5\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904628
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 210, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '210.9', 'subgroup_hash': 9, 'subgroup_order': 210, 'subgroup_tex': 'C_5\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904629
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 105, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '210.10', 'subgroup_hash': 10, 'subgroup_order': 210, 'subgroup_tex': 'C_7\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 79904630
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 105, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '210.10', 'subgroup_hash': 10, 'subgroup_order': 210, 'subgroup_tex': 'C_7\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 79904631
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 105, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '210.7', 'subgroup_hash': 7, 'subgroup_order': 210, 'subgroup_tex': 'C_3\\times D_{35}', 'supersolvable': True, 'sylow': 0}
  • id: 79904632
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 105, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '210.7', 'subgroup_hash': 7, 'subgroup_order': 210, 'subgroup_tex': 'C_3\\times D_{35}', 'supersolvable': True, 'sylow': 0}
  • id: 79904633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 168, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.50', 'subgroup_hash': 50, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.50', 'subgroup_hash': 50, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 84, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 84, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.31', 'subgroup_hash': 31, 'subgroup_order': 168, 'subgroup_tex': 'C_7\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 79904640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 84, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 79904641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 140, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '140.10', 'subgroup_hash': 10, 'subgroup_order': 140, 'subgroup_tex': 'D_{70}', 'supersolvable': True, 'sylow': 0}
  • id: 79904642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 140, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '140.10', 'subgroup_hash': 10, 'subgroup_order': 140, 'subgroup_tex': 'D_{70}', 'supersolvable': True, 'sylow': 0}
  • id: 79904643
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 140, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '140.4', 'subgroup_hash': 4, 'subgroup_order': 140, 'subgroup_tex': 'C_{140}', 'supersolvable': True, 'sylow': 0}
  • id: 79904644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 70, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.8', 'subgroup_hash': 8, 'subgroup_order': 140, 'subgroup_tex': 'C_5\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 70, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.9', 'subgroup_hash': 9, 'subgroup_order': 140, 'subgroup_tex': 'C_7\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 70, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.9', 'subgroup_hash': 9, 'subgroup_order': 140, 'subgroup_tex': 'C_7\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904648
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 70, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.2', 'subgroup_hash': 2, 'subgroup_order': 140, 'subgroup_tex': 'C_7:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 35, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.7', 'subgroup_hash': 7, 'subgroup_order': 140, 'subgroup_tex': 'D_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 35, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.7', 'subgroup_hash': 7, 'subgroup_order': 140, 'subgroup_tex': 'D_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 35, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.7', 'subgroup_hash': 7, 'subgroup_order': 140, 'subgroup_tex': 'D_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 35, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.12.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '140.7', 'subgroup_hash': 7, 'subgroup_order': 140, 'subgroup_tex': 'D_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': True, 'core_order': 120, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.28', 'subgroup_hash': 28, 'subgroup_order': 120, 'subgroup_tex': 'D_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 79904654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 60, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.12', 'subgroup_hash': 12, 'subgroup_order': 120, 'subgroup_tex': 'C_3:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.12', 'subgroup_hash': 12, 'subgroup_order': 120, 'subgroup_tex': 'C_3:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, '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': '120.18', 'subgroup_hash': 18, 'subgroup_order': 120, 'subgroup_tex': 'C_3\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1680.826.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.31', 'subgroup_hash': 31, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904662
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 105, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 105, 'label': '1680.826.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '105.2', 'subgroup_hash': 2, 'subgroup_order': 105, 'subgroup_tex': 'C_{105}', 'supersolvable': True, 'sylow': 0}
  • id: 79904663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 84, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 79904664
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 84, 'counter': 65, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 79904665
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 84, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 42, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 42, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 42, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 42, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.20.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '1680.826.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, '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': '80.37', 'subgroup_hash': 37, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904676
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 70, 'counter': 76, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '70.4', 'subgroup_hash': 4, 'subgroup_order': 70, 'subgroup_tex': 'C_{70}', 'supersolvable': True, 'sylow': 0}
  • id: 79904677
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 35, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.2', 'subgroup_hash': 2, 'subgroup_order': 70, 'subgroup_tex': 'C_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904678
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 35, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.2', 'subgroup_hash': 2, 'subgroup_order': 70, 'subgroup_tex': 'C_5\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904679
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 35, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.1', 'subgroup_hash': 1, 'subgroup_order': 70, 'subgroup_tex': 'C_7\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904681
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 35, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.1', 'subgroup_hash': 1, 'subgroup_order': 70, 'subgroup_tex': 'C_7\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904682
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 35, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.3', 'subgroup_hash': 3, 'subgroup_order': 70, 'subgroup_tex': 'D_{35}', 'supersolvable': True, 'sylow': 0}
  • id: 79904683
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 35, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, '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': '70.3', 'subgroup_hash': 3, 'subgroup_order': 70, 'subgroup_tex': 'D_{35}', 'supersolvable': True, 'sylow': 0}
  • id: 79904684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 60, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 79904685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 60, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.28.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 79904686
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 60, 'counter': 85, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 79904687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904690
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.28.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 28, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 14, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 14, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 28, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 28, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 79904489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1680.826.35.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '35.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 35, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904490
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 42, 'counter': 102, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 79904491
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 42, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904492
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 42, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1680.826.40.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904493
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 21, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904494
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 21, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.40.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904495
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 21, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904496
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 21, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.40.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 79904499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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: 79904500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 20, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 20, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904505
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 35, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 35, 'label': '1680.826.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '35.1', 'subgroup_hash': 1, 'subgroup_order': 35, 'subgroup_tex': 'C_{35}', 'supersolvable': True, 'sylow': 0}
  • id: 79904506
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 30, 'counter': 117, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 79904507
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904508
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904510
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 15, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 79904511
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 15, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 79904512
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904513
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.56.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79904514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 28, 'counter': 124, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 79904515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 14, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 14, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 14, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904521
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 14, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 7, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.60.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 12, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 12, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 79904533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.70.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '70.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 21, 'counter': 142, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1680.826.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 79904535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 20, 'counter': 143, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 10, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 10, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79904543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.84.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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: 79904547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1680.826.105.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '105.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 105, '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': 2}
  • id: 79904548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 15, 'counter': 155, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '1680.826.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 79904549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 14, 'counter': 156, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904550
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 7, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904551
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 7, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904552
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904554
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 79904555
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904556
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 79904557
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 420, 'characteristic': True, 'core_order': 12, 'counter': 163, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.140.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '140.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '140.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 140, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 79904558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 6, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 6, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '140.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '140.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904563
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.140.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904569
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 10, 'counter': 174, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79904570
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904571
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904572
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 5, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904573
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 5, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.168.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904574
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 5, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904576
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 5, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.168.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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: 79904577
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904579
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.210.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, '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: 79904584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 7, 'counter': 188, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1680.826.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{20}', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 79904585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 6, 'counter': 189, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.280.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '280.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '280.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 280, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904587
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 3, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.280.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904588
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 3, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.280.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904589
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.280.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 3, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.280.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 79904591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.280.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '280.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 195, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.280.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '280.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 79904593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 5, 'counter': 196, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '1680.826.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.150', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 150, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 79904594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 4, 'counter': 197, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.420.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '420.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '420.30', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 420, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79904595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904599
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.420.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1680.826.420.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, '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: 79904607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 840, 'characteristic': True, 'core_order': 3, 'counter': 208, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1680.826.560.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '560.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '560.120', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 120, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 560, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7\\times D_{20}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 79904608
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1680, 'characteristic': True, 'core_order': 2, 'counter': 209, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1680.826.840.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '840.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '840.175', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 175, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 840, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79904610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904611
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904612
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904613
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904614
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904615
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1680.826.840.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, '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: 79904616
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1680.826', 'ambient_counter': 826, 'ambient_order': 1680, 'ambient_tex': 'C_{140}:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1680, 'characteristic': True, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1680.826.1680.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1680.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1680.826', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 826, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1680, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{140}:D_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 79904486
    {'ambient': '1680.826', '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': '840.a1.a1', 'complements': ['1680.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '5.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7236, 4308, 7867, 5508, 3412, 6429, 6771, 5291], 'generators': [1, 1008, 420, 840, 2, 240, 1120], 'label': '1680.826.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '840.175'}
  • id: 79904487
    {'ambient': '1680.826', 'aut_centralizer_order': 40, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 40, 'centralizer': '84.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1', '20.a1.a1', '28.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2807, 8955, 3775, 922, 7110, 738, 3576, 566], 'generators': [3, 1008, 1120, 840, 240], 'label': '1680.826.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904488
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '336.125', 'aut_weyl_index': 240, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.e1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '60.d1.b1', '210.e1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7828, -1, 8406, -1, 1556, -1, 8186, -1], 'generators': [1, 840, 240, 420], 'label': '1680.826.30.e1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904489
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '35.a1', 'aut_quo_index': None, 'aut_stab_index': 35, 'aut_weyl_group': '96.209', 'aut_weyl_index': 840, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '7.a1.a1'], 'contains': ['70.a1.a1', '70.a1.b1', '70.b1.a1', '70.c1.a1', '70.c1.b1', '70.d1.a1', '70.e1.a1', '105.a1.a1'], 'core': '140.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [8666, -1, 9235, -1, 499, -1, 8991, -1], 'generators': [1, 1120, 2, 420, 840], 'label': '1680.826.35.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '35.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '35.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904490
    {'ambient': '1680.826', 'aut_centralizer_order': 6720, 'aut_label': '40.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 6720, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1', '20.d1.b1', '20.e1.a1', '20.e1.b1'], 'contains': ['80.a1.a1', '120.a1.a1', '280.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5399, 7355, 5516, 3704, 4900, 4962, 5195, 4971], 'generators': [840, 240, 1120], 'label': '1680.826.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 40, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1', '280.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904491
    {'ambient': '1680.826', 'aut_centralizer_order': 160, 'aut_label': '40.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '84.a1.a1', 'complements': ['42.d1.a1', '42.e1.a1', '42.c1.a1', '42.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1', '20.f1.a1', '20.f1.b1'], 'contains': ['80.a1.a1', '120.b1.a1', '280.b1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2359, 8965, 1936, 1719, 7436, 2572, 1859, 3505], 'generators': [3, 240, 1120], 'label': '1680.826.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904492
    {'ambient': '1680.826', 'aut_centralizer_order': 160, 'aut_label': '40.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '84.a1.a1', 'complements': ['42.d1.a1', '42.e1.a1', '42.c1.a1', '42.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '20.a1.a1', '20.f1.c1', '20.f1.d1'], 'contains': ['80.a1.a1', '120.b1.b1', '280.b1.b1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2359, 8965, 1241, 1024, 7436, 2572, 1750, 2922], 'generators': [1563, 240, 1120], 'label': '1680.826.40.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': ['8.b1.b1', '20.a1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.b1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904493
    {'ambient': '1680.826', 'aut_centralizer_order': 112, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2240, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.d1.a1', '20.f1.a1', '20.f1.c1'], 'contains': ['80.a1.a1', '120.c1.a1', '280.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1804, -1, 901, -1, 7206, -1, 1167, -1], 'generators': [2, 1120, 240], 'label': '1680.826.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904494
    {'ambient': '1680.826', 'aut_centralizer_order': 112, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2240, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '20.d1.b1', '20.f1.b1', '20.f1.d1'], 'contains': ['80.a1.a1', '120.c1.b1', '280.c1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1804, -1, 2860, -1, 7206, -1, 3556, -1], 'generators': [198, 1120, 240], 'label': '1680.826.40.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '40.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904495
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.e1.a1', '20.f1.b1', '20.f1.d1'], 'contains': ['80.a1.a1', '120.d1.a1', '280.d1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1525, -1, 2699, -1, 7667, -1, 3389, -1], 'generators': [949, 240, 1120], 'label': '1680.826.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '40.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904496
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '20.e1.b1', '20.f1.a1', '20.f1.c1'], 'contains': ['80.a1.a1', '120.d1.b1', '280.d1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1525, -1, 1062, -1, 7667, -1, 1334, -1], 'generators': [1, 240, 1120], 'label': '1680.826.40.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904497
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.a1', '84.d1.b1', '84.f1.a1', '84.f1.c1', '210.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3116, -1, 4778, -1, 7153, -1, 4609, -1], 'generators': [1, 840, 1008, 2], 'label': '1680.826.42.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904498
    {'ambient': '1680.826', 'aut_centralizer_order': 28, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1440.5913', 'aut_weyl_index': 56, 'centralizer': '120.a1.a1', 'complements': ['420.f1.b1', '420.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.d1.a1', '20.d1.a1', '28.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4207, 3238, 5518, 8000, 6381, 6830, 4767, 7569], 'generators': [2, 240, 1120, 840, 1008], 'label': '1680.826.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904499
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '14.b1.b1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.b1', '84.d1.a1', '84.f1.b1', '84.f1.d1', '210.a1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3116, -1, 5805, -1, 7153, -1, 6063, -1], 'generators': [949, 840, 1008, 198], 'label': '1680.826.42.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904500
    {'ambient': '1680.826', 'aut_centralizer_order': 240, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.10', 'aut_weyl_index': 5040, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.e1.a1', '210.b1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7349, -1, 9913, -1, 2642, -1, 9745, -1], 'generators': [3, 1008, 840, 420], 'label': '1680.826.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904501
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1', '84.e1.a1', '210.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6074, -1, 8131, -1, 4119, -1, 9141, -1], 'generators': [949, 840, 1008, 2], 'label': '1680.826.42.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904502
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '14.d1.b1', '21.a1.a1'], 'contains': ['84.c1.b1', '84.d1.b1', '84.e1.a1', '210.c1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6074, -1, 7741, -1, 4119, -1, 7107, -1], 'generators': [1, 840, 1008, 198], 'label': '1680.826.42.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904503
    {'ambient': '1680.826', 'aut_centralizer_order': 168, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.207', 'aut_weyl_index': 504, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.c1.a1', '84.c1.b1', '210.d1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9549, -1, 8656, -1, 2201, -1, 7968, -1], 'generators': [2, 840, 1008, 420], 'label': '1680.826.42.d1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904504
    {'ambient': '1680.826', 'aut_centralizer_order': 72, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '160.207', 'aut_weyl_index': 504, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.d1.b1', '210.e1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7767, -1, 9538, -1, 2384, -1, 9031, -1], 'generators': [1, 840, 1008, 420], 'label': '1680.826.42.e1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904505
    {'ambient': '1680.826', 'aut_centralizer_order': 3360, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.9', 'aut_weyl_index': 3360, 'centralizer': '4.d1.a1', 'complements': ['35.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.b1.b1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.d1.b1'], 'contains': ['240.a1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [251, 6700, 520, 4055, 8829, 4279, 1502, 4624], 'generators': [1008, 240], 'label': '1680.826.48.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['240.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904506
    {'ambient': '1680.826', 'aut_centralizer_order': 10080, 'aut_label': '56.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 10080, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.a1.b1', '28.b1.a1', '28.c1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1'], 'contains': ['112.a1.a1', '168.a1.a1', '280.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3788, 2646, 6603, 6415, 5948, 6463, 6191, 6326], 'generators': [840, 1008, 1120], 'label': '1680.826.56.a1.a1', 'mobius_quo': -1, 'mobius_sub': 56, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1', '28.a1.b1', '28.b1.a1'], 'normal_contains': ['112.a1.a1', '168.a1.a1', '280.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904507
    {'ambient': '1680.826', 'aut_centralizer_order': 240, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.5', 'aut_weyl_index': 3360, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.c1.a1', '28.f1.a1', '28.f1.b1'], 'contains': ['112.a1.a1', '168.b1.a1', '280.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [829, -1, 2978, -1, 8311, -1, 2836, -1], 'generators': [3, 1120, 1008], 'label': '1680.826.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904508
    {'ambient': '1680.826', 'aut_centralizer_order': 240, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.5', 'aut_weyl_index': 3360, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '28.c1.a1', '28.f1.c1', '28.f1.d1'], 'contains': ['112.a1.a1', '168.b1.b1', '280.b1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [829, -1, 2187, -1, 8311, -1, 2671, -1], 'generators': [1563, 1120, 1008], 'label': '1680.826.56.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904509
    {'ambient': '1680.826', 'aut_centralizer_order': 28, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1440.5913', 'aut_weyl_index': 56, 'centralizer': '120.a1.a1', 'complements': ['420.f1.a1', '420.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.b1', '12.d1.b1', '20.d1.b1', '28.a1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4207, 3238, 5292, 5219, 6381, 6830, 4532, 5239], 'generators': [198, 240, 1120, 840, 1008], 'label': '1680.826.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '28.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904510
    {'ambient': '1680.826', 'aut_centralizer_order': 168, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.f1.a1', '28.f1.c1'], 'contains': ['112.a1.a1', '168.c1.a1', '280.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [441, -1, 1691, -1, 8081, -1, 2167, -1], 'generators': [2, 1008, 1120], 'label': '1680.826.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904511
    {'ambient': '1680.826', 'aut_centralizer_order': 168, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '28.a1.b1', '28.f1.b1', '28.f1.d1'], 'contains': ['112.a1.a1', '168.c1.b1', '280.c1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [441, -1, 3444, -1, 8081, -1, 4169, -1], 'generators': [198, 1008, 1120], 'label': '1680.826.56.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '56.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904512
    {'ambient': '1680.826', 'aut_centralizer_order': 72, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.d1.a1', '28.f1.b1', '28.f1.d1'], 'contains': ['112.a1.a1', '168.d1.a1', '280.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [122, -1, 3668, -1, 8589, -1, 3832, -1], 'generators': [949, 1008, 1120], 'label': '1680.826.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '56.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904513
    {'ambient': '1680.826', 'aut_centralizer_order': 72, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '28.d1.b1', '28.f1.a1', '28.f1.c1'], 'contains': ['112.a1.a1', '168.d1.b1', '280.d1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [122, -1, 1824, -1, 8589, -1, 2305, -1], 'generators': [1, 1008, 1120], 'label': '1680.826.56.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904514
    {'ambient': '1680.826', 'aut_centralizer_order': 6720, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 6720, 'centralizer': '4.d1.a1', 'complements': ['28.f1.a1', '28.f1.c1', '28.f1.b1', '28.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.b1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.a1.a1', '420.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8676, 4205, 8584, 8352, 1999, 7214, 7751, 6901], 'generators': [420, 840, 240], 'label': '1680.826.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 30, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.b1.a1', '20.b1.a1'], 'normal_contains': ['120.a1.a1', '420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904515
    {'ambient': '1680.826', 'aut_centralizer_order': 320, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '42.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.a1.a1', '30.a1.a1', '30.a1.b1', '30.b1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.b1.b1', '420.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4232, -1, 4131, -1, 5766, -1, 4477, -1], 'generators': [3, 240, 840], 'label': '1680.826.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904516
    {'ambient': '1680.826', 'aut_centralizer_order': 224, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.5', 'aut_weyl_index': 6720, 'centralizer': '60.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.d1.a1', '30.a1.a1', '30.c1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '120.c1.a1', '420.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5139, -1, 5433, -1, 5326, -1, 5549, -1], 'generators': [2, 240, 840], 'label': '1680.826.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904517
    {'ambient': '1680.826', 'aut_centralizer_order': 224, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '12.5', 'aut_weyl_index': 6720, 'centralizer': '60.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '20.d1.b1', '30.a1.b1', '30.c1.b1', '30.d1.a1'], 'contains': ['120.a1.a1', '120.c1.b1', '420.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5139, -1, 5240, -1, 5326, -1, 5349, -1], 'generators': [198, 240, 840], 'label': '1680.826.60.c1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904518
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '140.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.e1.a1', '30.a1.b1', '30.c1.a1', '30.e1.a1'], 'contains': ['120.a1.a1', '120.d1.a1', '420.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5809, -1, 6392, -1, 5584, -1, 6409, -1], 'generators': [949, 240, 840], 'label': '1680.826.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904519
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '140.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.e1.b1', '30.a1.a1', '30.c1.b1', '30.e1.a1'], 'contains': ['120.a1.a1', '120.d1.b1', '420.d1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5809, -1, 4386, -1, 5584, -1, 4696, -1], 'generators': [1, 240, 840], 'label': '1680.826.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904520
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '280.a1.a1', 'complements': ['420.f1.a1', '420.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '12.a1.a1', '20.e1.a1', '28.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2441, 5088, 6343, 6609, 6745, 5311, 5503, 6404], 'generators': [949, 1120, 1008, 840, 240], 'label': '1680.826.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904521
    {'ambient': '1680.826', 'aut_centralizer_order': 320, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '84.7', 'aut_weyl_index': 960, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.c1.a1', '30.b1.a1', '30.c1.a1', '30.c1.b1'], 'contains': ['120.a1.a1', '420.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6830, -1, 7444, -1, 3732, -1, 7640, -1], 'generators': [1063, 240, 840], 'label': '1680.826.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904522
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '420.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '20.f1.a1', '30.a1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.d1.b1', '420.f1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2258, -1, 776, -1, 7899, -1, 1640, -1], 'generators': [1, 240, 2], 'label': '1680.826.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904523
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '420.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '20.f1.b1', '30.a1.b1'], 'contains': ['120.b1.a1', '120.c1.b1', '120.d1.a1', '420.f1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2258, -1, 2869, -1, 7899, -1, 3251, -1], 'generators': [277, 240, 198], 'label': '1680.826.60.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '60.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904524
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '420.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.c1', '20.f1.c1', '30.a1.a1'], 'contains': ['120.b1.b1', '120.c1.a1', '120.d1.b1', '420.f1.c1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2258, -1, 356, -1, 7899, -1, 911, -1], 'generators': [1561, 240, 2], 'label': '1680.826.60.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904525
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '420.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.d1', '20.f1.d1', '30.a1.b1'], 'contains': ['120.b1.b1', '120.c1.b1', '120.d1.a1', '420.f1.d1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2258, -1, 2468, -1, 7899, -1, 3694, -1], 'generators': [397, 240, 198], 'label': '1680.826.60.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '60.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.d1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904526
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '70.a1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3360, 'centralizer': '420.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '14.b1.a1', '35.a1.a1'], 'contains': ['140.b1.a1', '140.c1.a1', '140.d1.b1', '140.f1.a1', '140.f1.c1', '210.a1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [4953, -1, 4716, -1, 4713, -1, 4801, -1], 'generators': [1, 2, 840, 1120], 'label': '1680.826.70.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904527
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '70.a1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3360, 'centralizer': '420.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '14.b1.b1', '35.a1.a1'], 'contains': ['140.b1.a1', '140.c1.b1', '140.d1.a1', '140.f1.b1', '140.f1.d1', '210.a1.b1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [4953, -1, 6853, -1, 4713, -1, 6256, -1], 'generators': [277, 198, 840, 1120], 'label': '1680.826.70.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.a1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904528
    {'ambient': '1680.826', 'aut_centralizer_order': 480, 'aut_label': '70.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3360, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '14.c1.a1', '35.a1.a1'], 'contains': ['140.a1.a1', '140.b1.a1', '140.e1.a1', '210.b1.a1'], 'core': '140.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8056, -1, 9930, -1, 583, -1, 9928, -1], 'generators': [3, 420, 840, 1120], 'label': '1680.826.70.b1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '70.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904529
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '70.c1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3360, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '14.d1.a1', '35.a1.a1'], 'contains': ['140.c1.a1', '140.d1.a1', '140.e1.a1', '210.c1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [6908, -1, 8348, -1, 3103, -1, 9588, -1], 'generators': [1621, 2, 840, 1120], 'label': '1680.826.70.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904530
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '70.c1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3360, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.b1', '14.d1.b1', '35.a1.a1'], 'contains': ['140.c1.b1', '140.d1.b1', '140.e1.a1', '210.c1.b1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [6908, -1, 7706, -1, 3103, -1, 7219, -1], 'generators': [337, 198, 840, 1120], 'label': '1680.826.70.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904531
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '280.a1.a1', 'complements': ['420.f1.b1', '420.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.b1', '12.a1.b1', '20.e1.b1', '28.d1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2441, 5088, 4517, 3828, 6745, 5311, 3794, 4074], 'generators': [1, 1120, 1008, 840, 240], 'label': '1680.826.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904532
    {'ambient': '1680.826', 'aut_centralizer_order': 336, 'aut_label': '70.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1680, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '14.a1.a1', '35.a1.a1'], 'contains': ['140.a1.a1', '140.c1.a1', '140.c1.b1', '210.d1.a1'], 'core': '140.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9717, -1, 9264, -1, 73, -1, 8441, -1], 'generators': [2, 420, 840, 1120], 'label': '1680.826.70.d1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '70.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904533
    {'ambient': '1680.826', 'aut_centralizer_order': 144, 'aut_label': '70.e1', 'aut_quo_index': None, 'aut_stab_index': 35, 'aut_weyl_group': '16.11', 'aut_weyl_index': 5040, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.e1.a1', '14.e1.a1', '35.a1.a1'], 'contains': ['140.a1.a1', '140.d1.a1', '140.d1.b1', '210.e1.a1'], 'core': '140.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [9015, -1, 9094, -1, 304, -1, 9279, -1], 'generators': [1, 420, 1120, 840], 'label': '1680.826.70.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79904534
    {'ambient': '1680.826', 'aut_centralizer_order': 6720, 'aut_label': '80.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 6720, 'centralizer': '4.d1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.b1.b1', '40.c1.a1', '40.c1.b1', '40.d1.a1', '40.d1.b1'], 'contains': ['240.a1.a1', '560.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1605, 8145, 1182, 2227, 7274, 3528, 1896, 4048], 'generators': [1120, 240], 'label': '1680.826.80.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.b1.b1'], 'normal_contains': ['240.a1.a1', '560.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904535
    {'ambient': '1680.826', 'aut_centralizer_order': 10080, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 10080, 'centralizer': '2.b1.a1', 'complements': ['20.f1.a1', '20.f1.c1', '20.f1.b1', '20.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.b1.a1', '42.b1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '420.a1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8598, 1243, 9718, 9289, 2384, 8716, 8168, 8361], 'generators': [420, 840, 1008], 'label': '1680.826.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 42, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.b1.a1', '28.b1.a1'], 'normal_contains': ['168.a1.a1', '420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '42.5', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904536
    {'ambient': '1680.826', 'aut_centralizer_order': 480, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.2', 'aut_weyl_index': 10080, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.c1.a1', '42.a1.a1', '42.a1.b1', '42.b1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1', '420.b1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2932, -1, 4980, -1, 6571, -1, 4952, -1], 'generators': [3, 1008, 840], 'label': '1680.826.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904537
    {'ambient': '1680.826', 'aut_centralizer_order': 336, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.a1.a1', '42.a1.a1', '42.c1.a1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '420.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3349, -1, 6268, -1, 6131, -1, 6300, -1], 'generators': [2, 1008, 840], 'label': '1680.826.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904538
    {'ambient': '1680.826', 'aut_centralizer_order': 336, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '28.a1.b1', '42.a1.b1', '42.c1.b1', '42.d1.a1'], 'contains': ['168.a1.a1', '168.c1.b1', '420.c1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3349, -1, 6713, -1, 6131, -1, 6082, -1], 'generators': [198, 1008, 840], 'label': '1680.826.84.c1.b1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904539
    {'ambient': '1680.826', 'aut_centralizer_order': 144, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.d1.a1', '42.a1.b1', '42.c1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '420.d1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4076, -1, 7099, -1, 6313, -1, 6696, -1], 'generators': [949, 1008, 840], 'label': '1680.826.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904540
    {'ambient': '1680.826', 'aut_centralizer_order': 144, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '40.12', 'aut_weyl_index': 2016, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '28.d1.b1', '42.a1.a1', '42.c1.b1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.b1', '420.d1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4076, -1, 5738, -1, 6313, -1, 5704, -1], 'generators': [1, 1008, 840], 'label': '1680.826.84.d1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904541
    {'ambient': '1680.826', 'aut_centralizer_order': 480, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.2', 'aut_weyl_index': 10080, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.e1.a1', '42.b1.a1', '42.c1.a1', '42.c1.b1'], 'contains': ['168.a1.a1', '420.e1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6167, -1, 7840, -1, 4017, -1, 7859, -1], 'generators': [1063, 840, 1008], 'label': '1680.826.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904542
    {'ambient': '1680.826', 'aut_centralizer_order': 840, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.220', 'aut_weyl_index': 840, 'centralizer': '4.d1.a1', 'complements': ['420.f1.a1', '420.f1.c1', '420.f1.b1', '420.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '20.b1.a1', '28.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9009, 1336, 8678, 9430, 2880, 8903, 6800, 9159], 'generators': [420, 1008, 240, 1120, 840], 'label': '1680.826.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1', '20.b1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904543
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.a1.a1'], 'contains': ['168.b1.a1', '168.c1.a1', '168.d1.b1', '420.f1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [876, -1, 1820, -1, 9020, -1, 2444, -1], 'generators': [1, 1008, 2], 'label': '1680.826.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904544
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '28.f1.b1', '42.a1.b1'], 'contains': ['168.b1.a1', '168.c1.b1', '168.d1.a1', '420.f1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [876, -1, 4142, -1, 9020, -1, 3971, -1], 'generators': [949, 1008, 198], 'label': '1680.826.84.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.b1', 'old_label': '84.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904545
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.c1', '28.f1.c1', '42.a1.a1'], 'contains': ['168.b1.b1', '168.c1.a1', '168.d1.b1', '420.f1.c1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [876, -1, 1356, -1, 9020, -1, 1968, -1], 'generators': [217, 1008, 2], 'label': '1680.826.84.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904546
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.d1', '28.f1.d1', '42.a1.b1'], 'contains': ['168.b1.b1', '168.c1.b1', '168.d1.a1', '420.f1.d1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [876, -1, 3707, -1, 9020, -1, 4279, -1], 'generators': [733, 1008, 198], 'label': '1680.826.84.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.b1', 'old_label': '84.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904547
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '105.a1', 'aut_quo_index': None, 'aut_stab_index': 105, 'aut_weyl_group': '16.11', 'aut_weyl_index': 5040, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '21.a1.a1', '35.a1.a1'], 'contains': ['210.a1.a1', '210.a1.b1', '210.b1.a1', '210.c1.a1', '210.c1.b1', '210.d1.a1', '210.e1.a1'], 'core': '420.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7961, -1, 8649, -1, 1044, -1, 9447, -1], 'generators': [1, 2, 420], 'label': '1680.826.105.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '105.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '105.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904548
    {'ambient': '1680.826', 'aut_centralizer_order': 10080, 'aut_label': '112.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 10080, 'centralizer': '4.d1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.b1.b1', '56.c1.a1', '56.c1.b1', '56.d1.a1', '56.d1.b1'], 'contains': ['336.a1.a1', '560.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [278, 4600, 2719, 3477, 8098, 5030, 2842, 5200], 'generators': [1120, 1008], 'label': '1680.826.112.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['336.a1.a1', '560.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '4.2', 'quotient_action_kernel': '28.2', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904549
    {'ambient': '1680.826', 'aut_centralizer_order': 13440, 'aut_label': '120.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13440, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1', '60.c1.b1', '60.d1.a1', '60.d1.b1', '60.e1.a1'], 'contains': ['240.a1.a1', '840.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5456, 5785, 5460, 5204, 5416, 5781, 5349, 5776], 'generators': [840, 240], 'label': '1680.826.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': -120, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.a1', '840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.12', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904550
    {'ambient': '1680.826', 'aut_centralizer_order': 320, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '42.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.b1.a1', '60.b1.a1', '60.f1.a1', '60.f1.b1'], 'contains': ['240.a1.a1', '840.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2593, -1, 1695, -1, 7786, -1, 1994, -1], 'generators': [3, 240], 'label': '1680.826.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904551
    {'ambient': '1680.826', 'aut_centralizer_order': 320, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '42.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '40.b1.b1', '60.b1.a1', '60.f1.c1', '60.f1.d1'], 'contains': ['240.a1.a1', '840.b1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2593, -1, 830, -1, 7786, -1, 1797, -1], 'generators': [1563, 240], 'label': '1680.826.120.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904552
    {'ambient': '1680.826', 'aut_centralizer_order': 224, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13440, 'centralizer': '60.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.c1.a1', '60.c1.a1', '60.f1.a1', '60.f1.c1'], 'contains': ['240.a1.a1', '840.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2086, -1, 333, -1, 7622, -1, 1611, -1], 'generators': [2, 240], 'label': '1680.826.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904553
    {'ambient': '1680.826', 'aut_centralizer_order': 40, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 40, 'centralizer': '84.a1.a1', 'complements': ['420.f1.a1', '420.f1.c1', '420.f1.b1', '420.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.a1.a1', '12.e1.a1', '20.c1.a1', '28.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5873, 6950, 7179, 2430, 4877, 3784, 6622, 2903], 'generators': [1063, 840, 1120, 1008, 240], 'label': '1680.826.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.a1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904554
    {'ambient': '1680.826', 'aut_centralizer_order': 224, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13440, 'centralizer': '60.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '40.c1.b1', '60.c1.b1', '60.f1.b1', '60.f1.d1'], 'contains': ['240.a1.a1', '840.c1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2086, -1, 2974, -1, 7622, -1, 3556, -1], 'generators': [198, 240], 'label': '1680.826.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '120.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904555
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '140.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.d1.a1', '60.d1.a1', '60.f1.b1', '60.f1.d1'], 'contains': ['240.a1.a1', '840.d1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1379, -1, 2479, -1, 7934, -1, 3389, -1], 'generators': [949, 240], 'label': '1680.826.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '120.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904556
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '42.1', 'aut_weyl_index': 1920, 'centralizer': '140.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '40.d1.b1', '60.d1.b1', '60.f1.a1', '60.f1.c1'], 'contains': ['240.a1.a1', '840.d1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1379, -1, 528, -1, 7934, -1, 1709, -1], 'generators': [1, 240], 'label': '1680.826.120.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '120.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 79904557
    {'ambient': '1680.826', 'aut_centralizer_order': 20160, 'aut_label': '140.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '4.d1.a1', 'complements': ['12.f1.a1', '12.f1.c1', '12.f1.b1', '12.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '28.b1.a1', '70.b1.a1', '70.d1.a1', '70.e1.a1'], 'contains': ['280.a1.a1', '420.a1.a1'], 'core': '140.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9483, 3946, 9264, 7258, 812, 7965, 8276, 7477], 'generators': [420, 1120, 840], 'label': '1680.826.140.a1.a1', 'mobius_quo': 0, 'mobius_sub': 70, 'normal_closure': '140.a1.a1', 'normal_contained_in': ['20.b1.a1', '28.b1.a1'], 'normal_contains': ['280.a1.a1', '420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '140.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '35.1', 'quotient_action_kernel_order': 35, 'quotient_fusion': None, 'short_label': '140.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904558
    {'ambient': '1680.826', 'aut_centralizer_order': 960, 'aut_label': '140.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6720, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '28.c1.a1', '70.a1.a1', '70.a1.b1', '70.b1.a1'], 'contains': ['280.a1.a1', '280.b1.a1', '280.b1.b1', '420.b1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4700, -1, 4926, -1, 4736, -1, 5097, -1], 'generators': [3, 840, 1120], 'label': '1680.826.140.b1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '140.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904559
    {'ambient': '1680.826', 'aut_centralizer_order': 672, 'aut_label': '140.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6720, 'centralizer': '60.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '28.a1.a1', '70.a1.a1', '70.c1.a1', '70.d1.a1'], 'contains': ['280.a1.a1', '280.c1.a1', '420.c1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4926, -1, 5799, -1, 4310, -1, 6597, -1], 'generators': [2, 840, 1120], 'label': '1680.826.140.c1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '140.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904560
    {'ambient': '1680.826', 'aut_centralizer_order': 672, 'aut_label': '140.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6720, 'centralizer': '60.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.b1', '28.a1.b1', '70.a1.b1', '70.c1.b1', '70.d1.a1'], 'contains': ['280.a1.a1', '280.c1.b1', '420.c1.b1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4926, -1, 7090, -1, 4310, -1, 6508, -1], 'generators': [198, 840, 1120], 'label': '1680.826.140.c1.b1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '140.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904561
    {'ambient': '1680.826', 'aut_centralizer_order': 288, 'aut_label': '140.d1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '140.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.a1', '28.d1.a1', '70.a1.b1', '70.c1.a1', '70.e1.a1'], 'contains': ['280.a1.a1', '280.d1.a1', '420.d1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [5468, -1, 7362, -1, 4523, -1, 6835, -1], 'generators': [949, 840, 1120], 'label': '1680.826.140.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '140.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904562
    {'ambient': '1680.826', 'aut_centralizer_order': 288, 'aut_label': '140.d1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '140.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.b1', '28.d1.b1', '70.a1.a1', '70.c1.b1', '70.e1.a1'], 'contains': ['280.a1.a1', '280.d1.b1', '420.d1.b1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [5468, -1, 5274, -1, 4523, -1, 5842, -1], 'generators': [1, 840, 1120], 'label': '1680.826.140.d1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '140.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904563
    {'ambient': '1680.826', 'aut_centralizer_order': 960, 'aut_label': '140.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6720, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '28.e1.a1', '70.b1.a1', '70.c1.a1', '70.c1.b1'], 'contains': ['280.a1.a1', '420.e1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6986, -1, 7918, -1, 3359, -1, 8057, -1], 'generators': [1063, 840, 1120], 'label': '1680.826.140.e1.a1', 'mobius_quo': None, 'mobius_sub': 10, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '140.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904564
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '5040.bh', 'aut_weyl_index': 16, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.b1', '12.f1.a1', '20.f1.a1', '28.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 1275, -1, 8897, -1, 1198, -1], 'generators': [1, 1120, 1008, 2, 240], 'label': '1680.826.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '420.30'}
  • id: 79904565
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '140.f1', 'aut_quo_index': None, 'aut_stab_index': 280, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '420.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.a1', '28.f1.a1', '70.a1.a1'], 'contains': ['280.b1.a1', '280.c1.a1', '280.d1.b1', '420.f1.a1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2281, -1, 2050, -1, 6993, -1, 2543, -1], 'generators': [1, 2, 1120], 'label': '1680.826.140.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '140.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904566
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '140.f1', 'aut_quo_index': None, 'aut_stab_index': 280, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '420.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.b1', '28.f1.b1', '70.a1.b1'], 'contains': ['280.b1.a1', '280.c1.b1', '280.d1.a1', '420.f1.b1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2281, -1, 4342, -1, 6993, -1, 4070, -1], 'generators': [277, 198, 1120], 'label': '1680.826.140.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.b1', 'old_label': '140.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904567
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '140.f1', 'aut_quo_index': None, 'aut_stab_index': 280, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '420.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.c1', '28.f1.c1', '70.a1.a1'], 'contains': ['280.b1.b1', '280.c1.a1', '280.d1.b1', '420.f1.c1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2281, -1, 1096, -1, 6993, -1, 2067, -1], 'generators': [1561, 2, 1120], 'label': '1680.826.140.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '140.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.f1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904568
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '140.f1', 'aut_quo_index': None, 'aut_stab_index': 280, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '420.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.d1', '28.f1.d1', '70.a1.b1'], 'contains': ['280.b1.b1', '280.c1.b1', '280.d1.a1', '420.f1.d1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2281, -1, 3627, -1, 6993, -1, 4378, -1], 'generators': [397, 198, 1120], 'label': '1680.826.140.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.b1', 'old_label': '140.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.f1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904569
    {'ambient': '1680.826', 'aut_centralizer_order': 20160, 'aut_label': '168.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 20160, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.b1.a1', '84.c1.a1', '84.c1.b1', '84.d1.a1', '84.d1.b1', '84.e1.a1'], 'contains': ['336.a1.a1', '840.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3556, 1970, 6463, 7797, 6131, 7146, 6007, 6823], 'generators': [840, 1008], 'label': '1680.826.168.a1.a1', 'mobius_quo': 1, 'mobius_sub': -168, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1', '840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '84.14', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904570
    {'ambient': '1680.826', 'aut_centralizer_order': 480, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.1', 'aut_weyl_index': 20160, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.b1.a1', '84.b1.a1', '84.f1.a1', '84.f1.b1'], 'contains': ['336.a1.a1', '840.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [882, -1, 2933, -1, 8425, -1, 2950, -1], 'generators': [3, 1008], 'label': '1680.826.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904571
    {'ambient': '1680.826', 'aut_centralizer_order': 480, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.1', 'aut_weyl_index': 20160, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '56.b1.b1', '84.b1.a1', '84.f1.c1', '84.f1.d1'], 'contains': ['336.a1.a1', '840.b1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [882, -1, 2115, -1, 8425, -1, 2646, -1], 'generators': [1563, 1008], 'label': '1680.826.168.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904572
    {'ambient': '1680.826', 'aut_centralizer_order': 336, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.c1.a1', '84.c1.a1', '84.f1.a1', '84.f1.c1'], 'contains': ['336.a1.a1', '840.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [605, -1, 1418, -1, 8262, -1, 2183, -1], 'generators': [2, 1008], 'label': '1680.826.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '168.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904573
    {'ambient': '1680.826', 'aut_centralizer_order': 336, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.c1.b1', '84.c1.b1', '84.f1.b1', '84.f1.d1'], 'contains': ['336.a1.a1', '840.c1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [605, -1, 3828, -1, 8262, -1, 3987, -1], 'generators': [198, 1008], 'label': '1680.826.168.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '168.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904574
    {'ambient': '1680.826', 'aut_centralizer_order': 144, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.d1.a1', '84.d1.a1', '84.f1.b1', '84.f1.d1'], 'contains': ['336.a1.a1', '840.d1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [118, -1, 3958, -1, 8589, -1, 3798, -1], 'generators': [949, 1008], 'label': '1680.826.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '168.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904575
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '5040.bh', 'aut_weyl_index': 16, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.a1', '8.c1.b1', '8.d1.a1', '12.f1.b1', '20.f1.b1', '28.f1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 2848, -1, 8897, -1, 2270, -1], 'generators': [949, 1120, 1008, 198, 240], 'label': '1680.826.4.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '420.30'}
  • id: 79904576
    {'ambient': '1680.826', 'aut_centralizer_order': 144, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '20.3', 'aut_weyl_index': 4032, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '56.d1.b1', '84.d1.b1', '84.f1.a1', '84.f1.c1'], 'contains': ['336.a1.a1', '840.d1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [118, -1, 1504, -1, 8589, -1, 2271, -1], 'generators': [1, 1008], 'label': '1680.826.168.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 79904577
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '210.a1', 'aut_quo_index': None, 'aut_stab_index': 210, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '42.a1.a1', '70.a1.a1', '105.a1.a1'], 'contains': ['420.b1.a1', '420.c1.a1', '420.d1.b1', '420.f1.a1', '420.f1.c1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [4193, -1, 4635, -1, 5074, -1, 4801, -1], 'generators': [1, 2, 840], 'label': '1680.826.210.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904578
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '210.a1', 'aut_quo_index': None, 'aut_stab_index': 210, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '210.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.b1', '42.a1.b1', '70.a1.b1', '105.a1.a1'], 'contains': ['420.b1.a1', '420.c1.b1', '420.d1.a1', '420.f1.b1', '420.f1.d1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [4193, -1, 5973, -1, 5074, -1, 5976, -1], 'generators': [277, 198, 840], 'label': '1680.826.210.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.a1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904579
    {'ambient': '1680.826', 'aut_centralizer_order': 960, 'aut_label': '210.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '42.b1.a1', '70.b1.a1', '105.a1.a1'], 'contains': ['420.a1.a1', '420.b1.a1', '420.e1.a1'], 'core': '420.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8000, -1, 9131, -1, 1769, -1, 8590, -1], 'generators': [3, 420], 'label': '1680.826.210.b1.a1', 'mobius_quo': None, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '210.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904580
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '210.c1', 'aut_quo_index': None, 'aut_stab_index': 210, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '42.c1.a1', '70.c1.a1', '105.a1.a1'], 'contains': ['420.c1.a1', '420.d1.a1', '420.e1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6673, -1, 7995, -1, 3564, -1, 8462, -1], 'generators': [1621, 2], 'label': '1680.826.210.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904581
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '210.c1', 'aut_quo_index': None, 'aut_stab_index': 210, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.b1', '42.c1.b1', '70.c1.b1', '105.a1.a1'], 'contains': ['420.c1.b1', '420.d1.b1', '420.e1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6673, -1, 7547, -1, 3564, -1, 7107, -1], 'generators': [337, 198], 'label': '1680.826.210.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904582
    {'ambient': '1680.826', 'aut_centralizer_order': 672, 'aut_label': '210.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 10080, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '42.d1.a1', '70.d1.a1', '105.a1.a1'], 'contains': ['420.a1.a1', '420.c1.a1', '420.c1.b1'], 'core': '420.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9621, -1, 8624, -1, 1365, -1, 7957, -1], 'generators': [2, 420], 'label': '1680.826.210.d1.a1', 'mobius_quo': None, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '210.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904583
    {'ambient': '1680.826', 'aut_centralizer_order': 288, 'aut_label': '210.e1', 'aut_quo_index': None, 'aut_stab_index': 35, 'aut_weyl_group': '8.3', 'aut_weyl_index': 10080, 'centralizer': '140.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '42.e1.a1', '70.e1.a1', '105.a1.a1'], 'contains': ['420.a1.a1', '420.d1.a1', '420.d1.b1'], 'core': '420.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7718, -1, 8871, -1, 1556, -1, 8374, -1], 'generators': [1, 420], 'label': '1680.826.210.e1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '210.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904584
    {'ambient': '1680.826', 'aut_centralizer_order': 13440, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13440, 'centralizer': '2.d1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.b1.b1', '120.c1.a1', '120.c1.b1', '120.d1.a1', '120.d1.b1'], 'contains': ['1680.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1544, 7261, 883, 2695, 7723, 4313, 1945, 4650], 'generators': [240], 'label': '1680.826.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1'], 'normal_contains': ['1680.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.28', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904585
    {'ambient': '1680.826', 'aut_centralizer_order': 40320, 'aut_label': '280.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '56.a1.a1', '140.a1.a1', '140.b1.a1', '140.c1.a1', '140.c1.b1', '140.d1.a1', '140.d1.b1', '140.e1.a1'], 'contains': ['560.a1.a1', '840.a1.a1'], 'core': '280.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5181, 4173, 6379, 5508, 4736, 6463, 6205, 6299], 'generators': [840, 1120], 'label': '1680.826.280.a1.a1', 'mobius_quo': 1, 'mobius_sub': -280, 'normal_closure': '280.a1.a1', 'normal_contained_in': ['40.a1.a1', '56.a1.a1', '140.a1.a1'], 'normal_contains': ['560.a1.a1', '840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '280.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '140.10', 'quotient_action_kernel_order': 140, 'quotient_fusion': None, 'short_label': '280.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904586
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '5040.bh', 'aut_weyl_index': 16, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.d1.b1', '12.f1.c1', '20.f1.c1', '28.f1.c1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 444, -1, 8897, -1, 830, -1], 'generators': [217, 1120, 1008, 2, 240], 'label': '1680.826.4.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.c1', 'subgroup_fusion': None, 'weyl_group': '420.30'}
  • id: 79904587
    {'ambient': '1680.826', 'aut_centralizer_order': 960, 'aut_label': '280.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '56.b1.a1', '140.b1.a1', '140.f1.a1', '140.f1.b1'], 'contains': ['560.a1.a1', '840.b1.a1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2671, -1, 3261, -1, 6963, -1, 3048, -1], 'generators': [3, 1120], 'label': '1680.826.280.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '280.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904588
    {'ambient': '1680.826', 'aut_centralizer_order': 960, 'aut_label': '280.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.b1', '56.b1.b1', '140.b1.a1', '140.f1.c1', '140.f1.d1'], 'contains': ['560.a1.a1', '840.b1.b1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2671, -1, 2050, -1, 6963, -1, 2744, -1], 'generators': [1563, 1120], 'label': '1680.826.280.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '280.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904589
    {'ambient': '1680.826', 'aut_centralizer_order': 672, 'aut_label': '280.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '60.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '56.c1.a1', '140.c1.a1', '140.f1.a1', '140.f1.c1'], 'contains': ['560.a1.a1', '840.c1.a1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1870, -1, 1298, -1, 6815, -1, 2359, -1], 'generators': [2, 1120], 'label': '1680.826.280.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '280.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904590
    {'ambient': '1680.826', 'aut_centralizer_order': 672, 'aut_label': '280.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13440, 'centralizer': '60.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.b1', '56.c1.b1', '140.c1.b1', '140.f1.b1', '140.f1.d1'], 'contains': ['560.a1.a1', '840.c1.b1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1870, -1, 3742, -1, 6815, -1, 4163, -1], 'generators': [198, 1120], 'label': '1680.826.280.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '280.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 79904591
    {'ambient': '1680.826', 'aut_centralizer_order': 288, 'aut_label': '280.d1', 'aut_quo_index': None, 'aut_stab_index': 140, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '140.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '56.d1.a1', '140.d1.a1', '140.f1.b1', '140.f1.d1'], 'contains': ['560.a1.a1', '840.d1.a1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1362, -1, 4048, -1, 7110, -1, 4075, -1], 'generators': [949, 1120], 'label': '1680.826.280.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.b1', 'old_label': '280.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904592
    {'ambient': '1680.826', 'aut_centralizer_order': 288, 'aut_label': '280.d1', 'aut_quo_index': None, 'aut_stab_index': 140, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '140.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.b1', '56.d1.b1', '140.d1.b1', '140.f1.a1', '140.f1.c1'], 'contains': ['560.a1.a1', '840.d1.b1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1362, -1, 1688, -1, 7110, -1, 2447, -1], 'generators': [1, 1120], 'label': '1680.826.280.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '280.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904593
    {'ambient': '1680.826', 'aut_centralizer_order': 20160, 'aut_label': '336.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 20160, 'centralizer': '2.b1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1', '168.c1.a1', '168.c1.b1', '168.d1.a1', '168.d1.b1'], 'contains': ['1680.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [262, 5961, 2737, 4086, 8262, 5576, 2803, 5619], 'generators': [1008], 'label': '1680.826.336.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['1680.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.35', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904594
    {'ambient': '1680.826', 'aut_centralizer_order': 40320, 'aut_label': '420.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '2.b1.a1', 'complements': ['4.f1.a1', '4.f1.c1', '4.f1.b1', '4.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '84.a1.a1', '140.a1.a1', '210.b1.a1', '210.d1.a1', '210.e1.a1'], 'contains': ['840.a1.a1'], 'core': '420.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8235, 3092, 8871, 8641, 1769, 7897, 8168, 7425], 'generators': [420], 'label': '1680.826.420.a1.a1', 'mobius_quo': 0, 'mobius_sub': -210, 'normal_closure': '420.a1.a1', 'normal_contained_in': ['60.a1.a1', '84.a1.a1', '140.a1.a1'], 'normal_contains': ['840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '420.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '210.9', 'quotient_action_kernel_order': 210, 'quotient_fusion': None, 'short_label': '420.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904595
    {'ambient': '1680.826', 'aut_centralizer_order': 1920, 'aut_label': '420.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '84.b1.a1', '140.b1.a1', '210.a1.a1', '210.a1.b1', '210.b1.a1'], 'contains': ['840.a1.a1', '840.b1.a1', '840.b1.b1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3842, -1, 4770, -1, 5242, -1, 4952, -1], 'generators': [3, 840], 'label': '1680.826.420.b1.a1', 'mobius_quo': None, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '420.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904596
    {'ambient': '1680.826', 'aut_centralizer_order': 1344, 'aut_label': '420.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '84.c1.a1', '140.c1.a1', '210.a1.a1', '210.c1.a1', '210.d1.a1'], 'contains': ['840.a1.a1', '840.c1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4772, -1, 6089, -1, 4906, -1, 6300, -1], 'generators': [2, 840], 'label': '1680.826.420.c1.a1', 'mobius_quo': None, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '420.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904597
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '840.a1.a1', 'complements': ['840.c1.b1', '840.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.b1', '4.f1.a1', '4.f1.c1', '6.b1.a1', '10.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3432, 5982, 4337, 5508, 6563, 5055, 3794, 3184], 'generators': [1, 240, 840, 1120, 2, 1008], 'label': '1680.826.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '840.175'}
  • id: 79904598
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '5040.bh', 'aut_weyl_index': 16, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.b1', '8.c1.b1', '8.d1.a1', '12.f1.d1', '20.f1.d1', '28.f1.d1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 2116, -1, 8897, -1, 2455, -1], 'generators': [733, 1120, 1008, 198, 240], 'label': '1680.826.4.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.d1', 'subgroup_fusion': None, 'weyl_group': '420.30'}
  • id: 79904599
    {'ambient': '1680.826', 'aut_centralizer_order': 1344, 'aut_label': '420.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '30.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1', '84.c1.b1', '140.c1.b1', '210.a1.b1', '210.c1.b1', '210.d1.a1'], 'contains': ['840.a1.a1', '840.c1.b1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4772, -1, 6702, -1, 4906, -1, 6111, -1], 'generators': [198, 840], 'label': '1680.826.420.c1.b1', 'mobius_quo': None, 'mobius_sub': -14, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '420.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904600
    {'ambient': '1680.826', 'aut_centralizer_order': 576, 'aut_label': '420.d1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '70.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.a1', '84.d1.a1', '140.d1.a1', '210.a1.b1', '210.c1.a1', '210.e1.a1'], 'contains': ['840.a1.a1', '840.d1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [5414, -1, 7145, -1, 5074, -1, 6553, -1], 'generators': [949, 840], 'label': '1680.826.420.d1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '420.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904601
    {'ambient': '1680.826', 'aut_centralizer_order': 576, 'aut_label': '420.d1', 'aut_quo_index': None, 'aut_stab_index': 70, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '70.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.b1', '84.d1.b1', '140.d1.b1', '210.a1.a1', '210.c1.b1', '210.e1.a1'], 'contains': ['840.a1.a1', '840.d1.b1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [5414, -1, 5992, -1, 5074, -1, 5774, -1], 'generators': [1, 840], 'label': '1680.826.420.d1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '420.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904602
    {'ambient': '1680.826', 'aut_centralizer_order': 1920, 'aut_label': '420.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '42.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '84.e1.a1', '140.e1.a1', '210.b1.a1', '210.c1.a1', '210.c1.b1'], 'contains': ['840.a1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6942, -1, 7751, -1, 3648, -1, 7859, -1], 'generators': [1063], 'label': '1680.826.420.e1.a1', 'mobius_quo': None, 'mobius_sub': -10, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '420.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904603
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': 840, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '84.f1.a1', '140.f1.a1', '210.a1.a1'], 'contains': ['840.b1.a1', '840.c1.a1', '840.d1.b1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2281, -1, 1869, -1, 7448, -1, 2542, -1], 'generators': [1, 2], 'label': '1680.826.420.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.a1.a1', 'old_label': '420.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904604
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': 840, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '210.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.b1', '84.f1.b1', '140.f1.b1', '210.a1.b1'], 'contains': ['840.b1.a1', '840.c1.b1', '840.d1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2281, -1, 4157, -1, 7448, -1, 3892, -1], 'generators': [277, 198], 'label': '1680.826.420.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.a1.b1', 'old_label': '420.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904605
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': 840, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.c1', '84.f1.c1', '140.f1.c1', '210.a1.a1'], 'contains': ['840.b1.b1', '840.c1.a1', '840.d1.b1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2281, -1, 1227, -1, 7448, -1, 2088, -1], 'generators': [1561, 2], 'label': '1680.826.420.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.a1.a1', 'old_label': '420.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904606
    {'ambient': '1680.826', 'aut_centralizer_order': 96, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': 840, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '210.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.d1', '84.f1.d1', '140.f1.d1', '210.a1.b1'], 'contains': ['840.b1.b1', '840.c1.b1', '840.d1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2281, -1, 3562, -1, 7448, -1, 4258, -1], 'generators': [397, 198], 'label': '1680.826.420.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.a1.b1', 'old_label': '420.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904607
    {'ambient': '1680.826', 'aut_centralizer_order': 40320, 'aut_label': '560.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 40320, 'centralizer': '2.e1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '112.a1.a1', '280.a1.a1', '280.b1.a1', '280.b1.b1', '280.c1.a1', '280.c1.b1', '280.d1.a1', '280.d1.b1'], 'contains': ['1680.a1.a1'], 'core': '560.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1755, 5389, 2854, 3477, 7110, 4962, 2891, 5147], 'generators': [1120], 'label': '1680.826.560.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '560.a1.a1', 'normal_contained_in': ['80.a1.a1', '112.a1.a1', '280.a1.a1'], 'normal_contains': ['1680.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '560.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '280.26', 'quotient_action_kernel_order': 280, 'quotient_fusion': None, 'short_label': '560.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79904608
    {'ambient': '1680.826', 'aut_centralizer_order': 80640, 'aut_label': '840.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '168.a1.a1', '280.a1.a1', '420.a1.a1', '420.b1.a1', '420.c1.a1', '420.c1.b1', '420.d1.a1', '420.d1.b1', '420.e1.a1'], 'contains': ['1680.a1.a1'], 'core': '840.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4912, 4173, 6224, 5938, 5074, 6463, 6111, 6299], 'generators': [840], 'label': '1680.826.840.a1.a1', 'mobius_quo': -1, 'mobius_sub': 840, 'normal_closure': '840.a1.a1', 'normal_contained_in': ['120.a1.a1', '168.a1.a1', '280.a1.a1', '420.a1.a1'], 'normal_contains': ['1680.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '840.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '1.1', 'quotient_action_kernel': '840.175', 'quotient_action_kernel_order': 840, 'quotient_fusion': None, 'short_label': '840.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904609
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': None, 'aut_weyl_index': 20, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1', '10.d1.a1', '10.e1.a1', '15.a1.a1', '35.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8307, -1, 8036, -1, 1634, -1, 7260, -1], 'generators': [1, 240, 420, 840, 2, 1120], 'label': '1680.826.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 79904610
    {'ambient': '1680.826', 'aut_centralizer_order': 1920, 'aut_label': '840.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '168.b1.a1', '280.b1.a1', '420.b1.a1', '420.f1.a1', '420.f1.b1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2671, -1, 2962, -1, 7428, -1, 2980, -1], 'generators': [3], 'label': '1680.826.840.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '840.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904611
    {'ambient': '1680.826', 'aut_centralizer_order': 1920, 'aut_label': '840.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.b1', '168.b1.b1', '280.b1.b1', '420.b1.a1', '420.f1.c1', '420.f1.d1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2671, -1, 2030, -1, 7428, -1, 2715, -1], 'generators': [1563], 'label': '1680.826.840.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '840.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904612
    {'ambient': '1680.826', 'aut_centralizer_order': 1344, 'aut_label': '840.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '168.c1.a1', '280.c1.a1', '420.c1.a1', '420.f1.a1', '420.f1.c1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1968, -1, 1388, -1, 7280, -1, 2359, -1], 'generators': [2], 'label': '1680.826.840.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '840.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904613
    {'ambient': '1680.826', 'aut_centralizer_order': 1344, 'aut_label': '840.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '30.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.b1', '168.c1.b1', '280.c1.b1', '420.c1.b1', '420.f1.b1', '420.f1.d1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1968, -1, 3608, -1, 7280, -1, 3987, -1], 'generators': [198], 'label': '1680.826.840.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '840.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904614
    {'ambient': '1680.826', 'aut_centralizer_order': 576, 'aut_label': '840.d1', 'aut_quo_index': None, 'aut_stab_index': 140, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '70.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '168.d1.a1', '280.d1.a1', '420.d1.a1', '420.f1.b1', '420.f1.d1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1239, -1, 3933, -1, 7575, -1, 3892, -1], 'generators': [949], 'label': '1680.826.840.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.b1', 'old_label': '840.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904615
    {'ambient': '1680.826', 'aut_centralizer_order': 576, 'aut_label': '840.d1', 'aut_quo_index': None, 'aut_stab_index': 140, 'aut_weyl_group': '1.1', 'aut_weyl_index': 80640, 'centralizer': '70.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '168.d1.b1', '280.d1.b1', '420.d1.b1', '420.f1.a1', '420.f1.c1'], 'contains': ['1680.a1.a1'], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1239, -1, 1688, -1, 7575, -1, 2447, -1], 'generators': [1], 'label': '1680.826.840.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '840.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904616
    {'ambient': '1680.826', 'aut_centralizer_order': None, 'aut_label': '1680.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '336.a1.a1', '560.a1.a1', '840.a1.a1', '840.b1.a1', '840.b1.b1', '840.c1.a1', '840.c1.b1', '840.d1.a1', '840.d1.b1'], 'contains': [], 'core': '1680.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1755, 5764, 2791, 3758, 7428, 5269, 2847, 5383], 'generators': [], 'label': '1680.826.1680.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1680.a1.a1', 'normal_contained_in': ['240.a1.a1', '336.a1.a1', '560.a1.a1', '840.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1680.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79904617
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '280.a1.a1', 'complements': ['280.c1.a1', '280.c1.b1', '280.b1.a1', '280.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '30.e1.a1', '42.e1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7539, 2531, 8372, 7337, 3752, 8067, 6921, 8518], 'generators': [1, 840, 1008, 420, 240], 'label': '1680.826.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904618
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.c1.a1', '12.d1.a1', '12.f1.a1', '12.f1.c1', '30.a1.a1', '42.a1.a1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3270, -1, 3933, -1, 7524, -1, 3328, -1], 'generators': [1, 840, 1008, 2, 240], 'label': '1680.826.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904619
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.b1', '12.f1.b1', '12.f1.d1', '30.a1.b1', '42.a1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3270, -1, 5009, -1, 7524, -1, 4285, -1], 'generators': [949, 840, 1008, 198, 240], 'label': '1680.826.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904620
    {'ambient': '1680.826', 'aut_centralizer_order': 40, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1090', 'aut_weyl_index': 120, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1', '30.b1.a1', '42.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6491, -1, 8605, -1, 4021, -1, 8056, -1], 'generators': [3, 1008, 840, 420, 240], 'label': '1680.826.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904621
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '30.c1.a1', '42.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5480, -1, 7045, -1, 5199, -1, 7054, -1], 'generators': [949, 840, 1008, 2, 240], 'label': '1680.826.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904622
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.d1.b1', '12.e1.a1', '30.c1.b1', '42.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5480, -1, 6760, -1, 5199, -1, 5936, -1], 'generators': [1, 840, 1008, 198, 240], 'label': '1680.826.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904623
    {'ambient': '1680.826', 'aut_centralizer_order': 28, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '960.11160', 'aut_weyl_index': 84, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.d1.b1', '30.d1.a1', '42.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9154, -1, 7675, -1, 3484, -1, 6256, -1], 'generators': [2, 240, 840, 420, 1008], 'label': '1680.826.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904624
    {'ambient': '1680.826', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1920.204530', 'aut_weyl_index': 42, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.b1.b1', '14.c1.a1', '14.d1.a1', '14.d1.b1', '14.e1.a1', '21.a1.a1', '35.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7306, -1, 9409, -1, 2544, -1, 8087, -1], 'generators': [1, 1008, 420, 840, 2, 1120], 'label': '1680.826.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904625
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '840.a1.a1', 'complements': ['840.c1.a1', '840.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.c1.a1', '4.f1.b1', '4.f1.d1', '6.b1.b1', '10.b1.b1', '14.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3432, 5982, 5157, 3993, 6563, 5055, 4532, 5291], 'generators': [949, 240, 840, 1120, 198, 1008], 'label': '1680.826.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '840.175'}
  • id: 79904626
    {'ambient': '1680.826', 'aut_centralizer_order': 1680, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '48.44', 'aut_weyl_index': 1680, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2882, 5359, 5740, 4617, 6891, 4962, 3881, 4971], 'generators': [840, 1008, 240, 1120], 'label': '1680.826.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904627
    {'ambient': '1680.826', 'aut_centralizer_order': 40, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.537', 'aut_weyl_index': 80, 'centralizer': '84.a1.a1', 'complements': ['210.d1.a1', '210.e1.a1', '210.c1.a1', '210.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.a1.a1', '24.b1.a1', '40.b1.a1', '56.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [778, 8706, 1720, 1852, 9233, 1489, 1198, 2503], 'generators': [3, 1120, 240, 1008], 'label': '1680.826.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904628
    {'ambient': '1680.826', 'aut_centralizer_order': 40, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1008.537', 'aut_weyl_index': 80, 'centralizer': '84.a1.a1', 'complements': ['210.d1.a1', '210.e1.a1', '210.c1.a1', '210.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.c1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.b1.b1', '40.b1.b1', '56.b1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [778, 8706, 714, 570, 9233, 1489, 830, 1430], 'generators': [1563, 1120, 240, 1008], 'label': '1680.826.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '40.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904629
    {'ambient': '1680.826', 'aut_centralizer_order': 28, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.802', 'aut_weyl_index': 112, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.a1', '4.f1.c1'], 'contains': ['16.a1.a1', '24.c1.a1', '40.c1.a1', '56.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 176, -1, 8897, -1, 258, -1], 'generators': [2, 1120, 1008, 240], 'label': '1680.826.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904630
    {'ambient': '1680.826', 'aut_centralizer_order': 28, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.802', 'aut_weyl_index': 112, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.f1.b1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.c1.b1', '40.c1.b1', '56.c1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1114, -1, 2568, -1, 8897, -1, 2270, -1], 'generators': [198, 1120, 1008, 240], 'label': '1680.826.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904631
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1680.934', 'aut_weyl_index': 48, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.b1', '4.f1.d1'], 'contains': ['16.a1.a1', '24.d1.a1', '40.d1.a1', '56.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [297, -1, 2071, -1, 9569, -1, 1899, -1], 'generators': [949, 1008, 240, 1120], 'label': '1680.826.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904632
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1680.934', 'aut_weyl_index': 48, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '4.f1.a1', '4.f1.c1'], 'contains': ['16.a1.a1', '24.d1.b1', '40.d1.b1', '56.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [297, -1, 370, -1, 9569, -1, 459, -1], 'generators': [1, 1008, 240, 1120], 'label': '1680.826.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904633
    {'ambient': '1680.826', 'aut_centralizer_order': 80, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 80, 'centralizer': '84.a1.a1', 'complements': ['168.c1.a1', '168.c1.b1', '168.d1.b1', '168.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.b1.a1', '70.b1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7955, 8311, 9081, 2641, 1478, 2257, 8257, 1731], 'generators': [3, 840, 1120, 420, 240], 'label': '1680.826.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904634
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 80, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.d1.a1', '20.e1.b1', '20.f1.a1', '20.f1.c1', '30.a1.a1', '70.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5135, -1, 4350, -1, 5537, -1, 4025, -1], 'generators': [1, 840, 1120, 2, 240], 'label': '1680.826.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 79904635
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 80, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.d1.b1', '20.e1.a1', '20.f1.b1', '20.f1.d1', '30.a1.b1', '70.a1.b1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5135, -1, 4920, -1, 5537, -1, 5272, -1], 'generators': [277, 840, 1120, 198, 240], 'label': '1680.826.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 79904636
    {'ambient': '1680.826', 'aut_centralizer_order': 20, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 20, 'centralizer': '84.a1.a1', 'complements': ['840.c1.a1', '840.c1.b1', '840.d1.b1', '840.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '6.c1.a1', '10.a1.a1', '14.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6530, 7989, 8598, 1484, 3599, 3409, 7468, 1921], 'generators': [3, 240, 1008, 840, 420, 1120], 'label': '1680.826.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904637
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 80, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.d1.a1', '20.e1.a1', '30.c1.a1', '70.c1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6423, -1, 7361, -1, 4312, -1, 7882, -1], 'generators': [1621, 840, 1120, 2, 240], 'label': '1680.826.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 79904638
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 80, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.d1.b1', '20.e1.b1', '30.c1.b1', '70.c1.b1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6423, -1, 6751, -1, 4312, -1, 6082, -1], 'generators': [337, 840, 1120, 198, 240], 'label': '1680.826.10.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
  • id: 79904639
    {'ambient': '1680.826', 'aut_centralizer_order': 56, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '288.992', 'aut_weyl_index': 280, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.d1.a1', '20.d1.b1', '30.d1.a1', '70.d1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9882, -1, 8052, -1, 806, -1, 7228, -1], 'generators': [2, 240, 840, 420, 1120], 'label': '1680.826.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904640
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 120, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.e1.a1', '20.e1.b1', '30.e1.a1', '70.e1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8527, -1, 8246, -1, 1142, -1, 7540, -1], 'generators': [1, 1120, 840, 420, 240], 'label': '1680.826.10.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904641
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1680.934', 'aut_weyl_index': 48, 'centralizer': '280.a1.a1', 'complements': ['140.f1.a1', '140.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.b1.b1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '60.d1.a1', '84.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3259, 5006, 5860, 6508, 7743, 5755, 5543, 6162], 'generators': [949, 1008, 240, 840], 'label': '1680.826.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904642
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1680.934', 'aut_weyl_index': 48, 'centralizer': '280.a1.a1', 'complements': ['140.f1.b1', '140.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.a1.a1', '6.b1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '24.d1.b1', '60.d1.b1', '84.d1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3259, 5006, 4008, 5414, 7743, 5755, 3463, 5579], 'generators': [1, 1008, 240, 840], 'label': '1680.826.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.c1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904643
    {'ambient': '1680.826', 'aut_centralizer_order': 1680, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.44', 'aut_weyl_index': 1680, 'centralizer': '4.d1.a1', 'complements': ['140.f1.a1', '140.f1.c1', '140.f1.b1', '140.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '60.a1.a1', '84.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8902, 2365, 8760, 8695, 2908, 8067, 7540, 8518], 'generators': [420, 240, 840, 1008], 'label': '1680.826.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904644
    {'ambient': '1680.826', 'aut_centralizer_order': 80, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.122', 'aut_weyl_index': 240, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.b1.b1', '60.b1.a1', '84.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2675, -1, 3813, -1, 8003, -1, 3307, -1], 'generators': [3, 1008, 240, 840], 'label': '1680.826.12.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904645
    {'ambient': '1680.826', 'aut_centralizer_order': 56, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '240.200', 'aut_weyl_index': 336, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '60.c1.a1', '84.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3724, -1, 5531, -1, 7483, -1, 4411, -1], 'generators': [2, 240, 1008, 840], 'label': '1680.826.12.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904646
    {'ambient': '1680.826', 'aut_centralizer_order': 56, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '240.200', 'aut_weyl_index': 336, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.b1.b1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.c1.b1', '60.c1.b1', '84.c1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3724, -1, 5337, -1, 7483, -1, 4210, -1], 'generators': [198, 240, 1008, 840], 'label': '1680.826.12.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904647
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '840.a1.a1', 'complements': ['840.c1.b1', '840.d1.b1', '840.b1.a1', '840.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '6.d1.a1', '10.c1.a1', '14.d1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5873, 4308, 7179, 6766, 4877, 6429, 7092, 6345], 'generators': [949, 240, 840, 1120, 2, 1008], 'label': '1680.826.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '840.175'}
  • id: 79904648
    {'ambient': '1680.826', 'aut_centralizer_order': 80, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.122', 'aut_weyl_index': 240, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '60.e1.a1', '84.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5628, -1, 6968, -1, 4381, -1, 7378, -1], 'generators': [1063, 840, 240, 1008], 'label': '1680.826.12.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904649
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.d1.b1', '60.f1.a1', '84.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 1073, -1, 9878, -1, 645, -1], 'generators': [1, 1008, 240, 2], 'label': '1680.826.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904650
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.b1.b1'], 'contains': ['24.b1.a1', '24.c1.b1', '24.d1.a1', '60.f1.b1', '84.f1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 2848, -1, 9878, -1, 2084, -1], 'generators': [949, 1008, 240, 198], 'label': '1680.826.12.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904651
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '6.b1.a1'], 'contains': ['24.b1.b1', '24.c1.a1', '24.d1.b1', '60.f1.c1', '84.f1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 430, -1, 9878, -1, 73, -1], 'generators': [217, 1008, 240, 2], 'label': '1680.826.12.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.c1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904652
    {'ambient': '1680.826', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '6.b1.b1'], 'contains': ['24.b1.b1', '24.c1.b1', '24.d1.a1', '60.f1.d1', '84.f1.d1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 2366, -1, 9878, -1, 2455, -1], 'generators': [733, 1008, 240, 198], 'label': '1680.826.12.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.d1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904653
    {'ambient': '1680.826', 'aut_centralizer_order': 84, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11038', 'aut_weyl_index': 84, 'centralizer': '120.a1.a1', 'complements': ['120.d1.b1', '120.d1.a1', '120.b1.a1', '120.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.a1.b1', '28.b1.a1', '42.d1.a1', '70.d1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9050, 369, 9560, 8196, 2019, 9697, 7384, 9768], 'generators': [2, 840, 1120, 420, 1008], 'label': '1680.826.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['28.a1.a1', '28.a1.b1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904654
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 168, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.c1.a1', '28.d1.b1', '28.f1.a1', '28.f1.c1', '42.a1.a1', '70.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3920, -1, 4741, -1, 5969, -1, 5013, -1], 'generators': [1, 840, 1120, 2, 1008], 'label': '1680.826.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904655
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 168, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.a1'], 'contains': ['28.a1.b1', '28.c1.a1', '28.d1.a1', '28.f1.b1', '28.f1.d1', '42.a1.b1', '70.a1.b1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [3920, -1, 6670, -1, 5969, -1, 5733, -1], 'generators': [949, 840, 1120, 198, 1008], 'label': '1680.826.14.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904656
    {'ambient': '1680.826', 'aut_centralizer_order': 120, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.206', 'aut_weyl_index': 840, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.c1.a1', '28.e1.a1', '42.b1.a1', '70.b1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6951, -1, 9866, -1, 2613, -1, 9173, -1], 'generators': [3, 1008, 840, 420, 1120], 'label': '1680.826.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904657
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 168, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.a1', '28.e1.a1', '42.c1.a1', '70.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6037, -1, 8365, -1, 4555, -1, 8833, -1], 'generators': [949, 840, 1120, 2, 1008], 'label': '1680.826.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904658
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '840.a1.a1', 'complements': ['840.c1.a1', '840.d1.a1', '840.b1.a1', '840.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.b1', '4.e1.a1', '6.d1.b1', '10.c1.b1', '14.d1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5873, 4308, 6895, 2734, 4877, 6429, 6082, 4238], 'generators': [1, 240, 840, 1120, 198, 1008], 'label': '1680.826.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '840.175'}
  • id: 79904659
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 168, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '7.a1.a1'], 'contains': ['28.a1.b1', '28.d1.b1', '28.e1.a1', '42.c1.b1', '70.c1.b1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6037, -1, 7541, -1, 4555, -1, 6430, -1], 'generators': [1, 840, 1120, 198, 1008], 'label': '1680.826.14.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904660
    {'ambient': '1680.826', 'aut_centralizer_order': 36, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 252, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.d1.a1', '28.d1.b1', '42.e1.a1', '70.e1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9310, -1, 9319, -1, 2279, -1, 8459, -1], 'generators': [1, 1120, 840, 420, 1008], 'label': '1680.826.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904661
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 120, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.a1.b1', '30.b1.a1', '30.c1.a1', '30.c1.b1', '30.d1.a1', '30.e1.a1', '105.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8085, -1, 7916, -1, 1788, -1, 7725, -1], 'generators': [1, 420, 840, 2, 240], 'label': '1680.826.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904662
    {'ambient': '1680.826', 'aut_centralizer_order': 1680, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '48.44', 'aut_weyl_index': 1680, 'centralizer': '4.d1.a1', 'complements': ['105.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '8.d1.b1'], 'contains': ['48.a1.a1', '80.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [422, 6834, 725, 2266, 8829, 4168, 1025, 4277], 'generators': [1120, 240, 1008], 'label': '1680.826.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['48.a1.a1', '80.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '1680.826', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904663
    {'ambient': '1680.826', 'aut_centralizer_order': 160, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '504.162', 'aut_weyl_index': 160, 'centralizer': '84.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.b1.b1', '60.b1.a1', '140.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4723, 9631, 4144, 1219, 5578, 2572, 3767, 3334], 'generators': [3, 1120, 240, 840], 'label': '1680.826.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '40.b1.a1', '40.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904664
    {'ambient': '1680.826', 'aut_centralizer_order': 3360, 'aut_label': '20.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 3360, 'centralizer': '4.d1.a1', 'complements': ['84.f1.a1', '84.f1.c1', '84.f1.b1', '84.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.a1.a1', '10.d1.a1', '10.e1.a1'], 'contains': ['40.a1.a1', '60.a1.a1', '140.a1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9777, 5389, 8811, 7594, 812, 6514, 8077, 6744], 'generators': [420, 240, 840, 1120], 'label': '1680.826.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.d1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1', '140.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904665
    {'ambient': '1680.826', 'aut_centralizer_order': 160, 'aut_label': '20.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '504.162', 'aut_weyl_index': 160, 'centralizer': '84.a1.a1', 'complements': ['84.f1.a1', '84.f1.c1', '84.f1.b1', '84.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.a1.a1', '10.c1.a1', '10.c1.b1'], 'contains': ['40.a1.a1', '60.e1.a1', '140.e1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6818, 8145, 7220, 3429, 3320, 3784, 7840, 4015], 'generators': [1063, 1120, 240, 840], 'label': '1680.826.20.c1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.c1.a1', 'normal_contained_in': ['4.e1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904666
    {'ambient': '1680.826', 'aut_centralizer_order': 112, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '72.48', 'aut_weyl_index': 1120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.b1.a1', '10.c1.a1', '10.d1.a1'], 'contains': ['40.a1.a1', '40.c1.a1', '60.c1.a1', '140.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5074, -1, 5116, -1, 5039, -1, 5698, -1], 'generators': [2, 240, 1120, 840], 'label': '1680.826.20.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904667
    {'ambient': '1680.826', 'aut_centralizer_order': 112, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '72.48', 'aut_weyl_index': 1120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.b1.b1', '10.c1.b1', '10.d1.a1'], 'contains': ['40.a1.a1', '40.c1.b1', '60.c1.b1', '140.c1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5074, -1, 5307, -1, 5039, -1, 5389, -1], 'generators': [198, 240, 1120, 840], 'label': '1680.826.20.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 79904668
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.b1.b1', '10.c1.a1', '10.e1.a1'], 'contains': ['40.a1.a1', '40.d1.a1', '60.d1.a1', '140.d1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5460, -1, 6653, -1, 5346, -1, 6654, -1], 'generators': [949, 1120, 240, 840], 'label': '1680.826.20.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904669
    {'ambient': '1680.826', 'aut_centralizer_order': 14, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 14, 'centralizer': '120.a1.a1', 'complements': ['840.d1.b1', '840.d1.a1', '840.b1.a1', '840.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.e1.a1', '10.d1.a1', '14.a1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9152, 982, 7926, 9266, 2880, 9160, 6448, 8439], 'generators': [2, 1008, 240, 840, 420, 1120], 'label': '1680.826.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904670
    {'ambient': '1680.826', 'aut_centralizer_order': 48, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '10.b1.a1', '10.c1.b1', '10.e1.a1'], 'contains': ['40.a1.a1', '40.d1.b1', '60.d1.b1', '140.d1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5460, -1, 4443, -1, 5346, -1, 4025, -1], 'generators': [1, 1120, 240, 840], 'label': '1680.826.20.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.e1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904671
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.b1.a1'], 'contains': ['40.b1.a1', '40.c1.a1', '40.d1.b1', '60.f1.a1', '140.f1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2047, -1, 1275, -1, 8311, -1, 1382, -1], 'generators': [1, 1120, 240, 2], 'label': '1680.826.20.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904672
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '10.b1.b1'], 'contains': ['40.b1.a1', '40.c1.b1', '40.d1.a1', '60.f1.b1', '140.f1.b1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2047, -1, 3201, -1, 8311, -1, 2623, -1], 'generators': [277, 1120, 240, 198], 'label': '1680.826.20.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '20.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904673
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '10.b1.a1'], 'contains': ['40.b1.b1', '40.c1.a1', '40.d1.b1', '60.f1.c1', '140.f1.c1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2047, -1, 1051, -1, 8311, -1, 1014, -1], 'generators': [1561, 1120, 240, 2], 'label': '1680.826.20.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.c1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904674
    {'ambient': '1680.826', 'aut_centralizer_order': 8, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '252.26', 'aut_weyl_index': 320, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '10.b1.b1'], 'contains': ['40.b1.b1', '40.c1.b1', '40.d1.a1', '60.f1.d1', '140.f1.d1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2047, -1, 2963, -1, 8311, -1, 2790, -1], 'generators': [397, 1120, 240, 198], 'label': '1680.826.20.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '20.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.d1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
  • id: 79904675
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 252, 'centralizer': '420.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.a1.b1', '42.b1.a1', '42.c1.a1', '42.c1.b1', '42.d1.a1', '42.e1.a1', '105.a1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7409, -1, 8717, -1, 3148, -1, 8660, -1], 'generators': [1, 420, 840, 2, 1008], 'label': '1680.826.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904676
    {'ambient': '1680.826', 'aut_centralizer_order': 3360, 'aut_label': '24.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '24.9', 'aut_weyl_index': 3360, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.a1.a1', '120.a1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3084, 3810, 5711, 5125, 6830, 5712, 4587, 5749], 'generators': [840, 240, 1008], 'label': '1680.826.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904677
    {'ambient': '1680.826', 'aut_centralizer_order': 80, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.8', 'aut_weyl_index': 480, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '120.b1.a1', '168.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1174, -1, 1644, -1, 9532, -1, 1502, -1], 'generators': [3, 240, 1008], 'label': '1680.826.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904678
    {'ambient': '1680.826', 'aut_centralizer_order': 80, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.8', 'aut_weyl_index': 480, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.f1.c1', '12.f1.d1'], 'contains': ['48.a1.a1', '120.b1.b1', '168.b1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1174, -1, 655, -1, 9532, -1, 772, -1], 'generators': [1563, 240, 1008], 'label': '1680.826.24.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904679
    {'ambient': '1680.826', 'aut_centralizer_order': 56, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.40', 'aut_weyl_index': 672, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.f1.a1', '12.f1.c1'], 'contains': ['48.a1.a1', '120.c1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [812, -1, 70, -1, 9251, -1, 495, -1], 'generators': [2, 1008, 240], 'label': '1680.826.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904680
    {'ambient': '1680.826', 'aut_centralizer_order': 6, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '280.a1.a1', 'complements': ['840.c1.a1', '840.c1.b1', '840.b1.a1', '840.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1', '6.a1.a1', '10.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8772, 2739, 8374, 7946, 3226, 7717, 6656, 7333], 'generators': [1, 240, 1120, 840, 420, 1008], 'label': '1680.826.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.c1.b1', '4.d1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '840.175', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904681
    {'ambient': '1680.826', 'aut_centralizer_order': 56, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.40', 'aut_weyl_index': 672, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.d1.b1', '12.f1.b1', '12.f1.d1'], 'contains': ['48.a1.a1', '120.c1.b1', '168.c1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [812, -1, 2451, -1, 9251, -1, 3112, -1], 'generators': [198, 1008, 240], 'label': '1680.826.24.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '24.c1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 79904682
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.f1.b1', '12.f1.d1'], 'contains': ['48.a1.a1', '120.d1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [135, -1, 2271, -1, 9763, -1, 2974, -1], 'generators': [949, 240, 1008], 'label': '1680.826.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.d1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904683
    {'ambient': '1680.826', 'aut_centralizer_order': 24, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '840.139', 'aut_weyl_index': 96, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.a1.b1', '12.f1.a1', '12.f1.c1'], 'contains': ['48.a1.a1', '120.d1.b1', '168.d1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [135, -1, 295, -1, 9763, -1, 633, -1], 'generators': [1, 240, 1008], 'label': '1680.826.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '140.7'}
  • id: 79904684
    {'ambient': '1680.826', 'aut_centralizer_order': 168, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '240.195', 'aut_weyl_index': 336, 'centralizer': '120.a1.a1', 'complements': ['60.f1.b1', '60.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.a1.a1', '14.b1.a1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.c1.a1', '84.c1.a1', '140.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3862, 2095, 6536, 7305, 6086, 7274, 6516, 7909], 'generators': [2, 1120, 1008, 840], 'label': '1680.826.28.a1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.b1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904685
    {'ambient': '1680.826', 'aut_centralizer_order': 168, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '240.195', 'aut_weyl_index': 336, 'centralizer': '120.a1.a1', 'complements': ['60.f1.a1', '60.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '14.a1.a1', '14.b1.b1', '14.d1.b1'], 'contains': ['56.a1.a1', '56.c1.b1', '84.c1.b1', '140.c1.b1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3862, 2095, 6804, 6008, 6086, 7274, 6407, 7327], 'generators': [198, 1120, 1008, 840], 'label': '1680.826.28.a1.b1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.b1', 'normal_contained_in': ['4.b1.b1', '14.a1.a1'], 'normal_contains': ['56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.b1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.a1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 79904686
    {'ambient': '1680.826', 'aut_centralizer_order': 5040, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 5040, 'centralizer': '4.d1.a1', 'complements': ['60.f1.a1', '60.f1.c1', '60.f1.b1', '60.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.a1.a1', '14.c1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '84.a1.a1', '140.a1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9438, 774, 9784, 8993, 2019, 8861, 8922, 9126], 'generators': [420, 1008, 840, 1120], 'label': '1680.826.28.b1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.d1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.a1.a1', '140.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '840.175', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79904687
    {'ambient': '1680.826', 'aut_centralizer_order': 240, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.35', 'aut_weyl_index': 1680, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.b1.a1', '14.b1.b1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.b1.b1', '84.b1.a1', '140.b1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3240, -1, 4859, -1, 6625, -1, 4996, -1], 'generators': [3, 1008, 1120, 840], 'label': '1680.826.28.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904688
    {'ambient': '1680.826', 'aut_centralizer_order': 72, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.b1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.d1.a1', '84.d1.a1', '140.d1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4095, -1, 7043, -1, 6317, -1, 6822, -1], 'generators': [949, 1120, 1008, 840], 'label': '1680.826.28.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904689
    {'ambient': '1680.826', 'aut_centralizer_order': 72, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '80.50', 'aut_weyl_index': 1008, 'centralizer': '280.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '14.b1.a1', '14.d1.b1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.d1.b1', '84.d1.b1', '140.d1.b1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4095, -1, 5794, -1, 6317, -1, 5882, -1], 'generators': [1, 1120, 1008, 840], 'label': '1680.826.28.d1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 79904690
    {'ambient': '1680.826', 'aut_centralizer_order': 240, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.35', 'aut_weyl_index': 1680, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.c1.a1', '14.d1.a1', '14.d1.b1'], 'contains': ['56.a1.a1', '84.e1.a1', '140.e1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6082, -1, 7912, -1, 3857, -1, 8766, -1], 'generators': [1063, 840, 1120, 1008], 'label': '1680.826.28.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 79904691
    {'ambient': '1680.826', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '15.a1.a1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7035, -1, 7578, -1, 4004, -1, 6887, -1], 'generators': [1, 240, 420, 840, 2, 1008], 'label': '1680.826.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '280.36'}
  • id: 79904692
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.b1.a1'], 'contains': ['56.b1.a1', '56.c1.a1', '56.d1.b1', '84.f1.a1', '140.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [853, -1, 1962, -1, 8589, -1, 1715, -1], 'generators': [1, 1120, 1008, 2], 'label': '1680.826.28.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.a1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904693
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '14.b1.b1'], 'contains': ['56.b1.a1', '56.c1.b1', '56.d1.a1', '84.f1.b1', '140.f1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [853, -1, 3591, -1, 8589, -1, 2956, -1], 'generators': [949, 1120, 1008, 198], 'label': '1680.826.28.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '28.f1.b1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904694
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.c1', '14.b1.a1'], 'contains': ['56.b1.b1', '56.c1.a1', '56.d1.b1', '84.f1.c1', '140.f1.c1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [853, -1, 1665, -1, 8589, -1, 1548, -1], 'generators': [217, 1120, 1008, 2], 'label': '1680.826.28.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.f1.c1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.c1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904695
    {'ambient': '1680.826', 'aut_centralizer_order': 12, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '120.36', 'aut_weyl_index': 672, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.d1', '14.b1.b1'], 'contains': ['56.b1.b1', '56.c1.b1', '56.d1.a1', '84.f1.d1', '140.f1.d1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [853, -1, 3288, -1, 8589, -1, 3123, -1], 'generators': [733, 1120, 1008, 198], 'label': '1680.826.28.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.b1', 'old_label': '28.f1.d1', 'projective_image': '1680.826', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.d1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 79904696
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '420.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.b1', '60.f1.a1', '60.f1.c1', '210.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4554, -1, 3955, -1, 5832, -1, 3615, -1], 'generators': [1, 840, 240, 2], 'label': '1680.826.30.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904697
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '420.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.b1', '60.d1.a1', '60.f1.b1', '60.f1.d1', '210.a1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4554, -1, 4636, -1, 5832, -1, 5192, -1], 'generators': [277, 840, 240, 198], 'label': '1680.826.30.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904698
    {'ambient': '1680.826', 'aut_centralizer_order': 160, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.e1.a1', '210.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8060, -1, 9124, -1, 1788, -1, 8580, -1], 'generators': [3, 840, 240, 420], 'label': '1680.826.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
  • id: 79904699
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.d1.a1', '60.e1.a1', '210.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6675, -1, 7587, -1, 3564, -1, 8314, -1], 'generators': [1621, 840, 240, 2], 'label': '1680.826.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904700
    {'ambient': '1680.826', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '168.47', 'aut_weyl_index': 480, 'centralizer': '840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '10.c1.b1', '15.a1.a1'], 'contains': ['60.c1.b1', '60.d1.b1', '60.e1.a1', '210.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6675, -1, 6277, -1, 3564, -1, 6979, -1], 'generators': [337, 840, 240, 198], 'label': '1680.826.30.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.b1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.b1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
  • id: 79904701
    {'ambient': '1680.826', 'aut_centralizer_order': 112, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1680, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.c1.b1', '210.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9225, -1, 8227, -1, 1325, -1, 7683, -1], 'generators': [2, 240, 840, 420], 'label': '1680.826.30.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '840.175', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}