Abstract group data - 120.25

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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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 2, 6], 'aut_gens': [[625630, 992, 178772], [566050, 992, 774572], [327708, 29760, 178772], [625630, 29760, 178772], [297922, 24180, 178772]], 'aut_group': '96.206', 'aut_hash': 206, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 11, 'aut_perms': [368046, 294, 1, 3996721], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 1, 4, 1], [10, 2, 4, 1], [10, 6, 4, 1], [15, 2, 4, 1], [20, 6, 4, 1], [30, 2, 4, 1], [30, 2, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{12}:C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 6, 1], [3, 2, 1], [4, 6, 1], [5, 1, 4], [6, 2, 3], [10, 1, 4], [10, 2, 4], [10, 6, 4], [15, 2, 4], [20, 6, 4], [30, 2, 12]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['24.8', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 1, 4, 1], [10, 2, 4, 1], [10, 6, 4, 1], [15, 2, 4, 1], [20, 6, 4, 1], [30, 2, 4, 1], [30, 2, 8, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 36, 'exponent': 60, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[2, 0, 8]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '60.11', 'hash': 25, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 2, 3], 'inner_gens': [[625630, 25172, 178772], [566050, 992, 774572], [625630, 24180, 178772]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 20], [2, 25]], 'label': '120.25', 'linC_count': 8, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 12, 'linQ_dim': 8, 'linQ_dim_count': 12, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:D4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 16, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 45, 'number_divisions': 16, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 32, 'number_subgroups': 60, 'old_label': None, 'order': 120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 9], [3, 2], [4, 6], [5, 4], [6, 6], [10, 36], [15, 8], [20, 24], [30, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [29792, 29792], 'outer_gens': [[357502, 992, 774572], [327708, 992, 178772]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 5], [8, 3], [16, 1]], 'representations': {'PC': {'code': 241835599572999, 'gens': [1, 2, 3], 'pres': [5, -2, -2, 2, -3, -5, 692, 42, 1763, 78]}, 'GLFp': {'d': 2, 'p': 31, 'gens': [625630, 992, 178772]}, 'Perm': {'d': 12, 'gens': [40280400, 7620480, 33, 87091200, 5760]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:D_4', 'transitive_degree': 60, '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: 108579212
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 25, 'group_order': 120, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 29792, 'size': 1}
  • id: 108579223
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 25, 'group_order': 120, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 893760, 'size': 1}
  • id: 108579234
    {'aut_label': '2B', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 25, 'group_order': 120, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 29821, 'size': 2}
  • id: 108579245
    {'aut_label': '2C', 'centralizer': '6.b1.a1', 'counter': 4, 'group_counter': 25, 'group_order': 120, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 992, 'size': 6}
  • id: 108579252
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 25, 'group_order': 120, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 148980, 'size': 2}
  • id: 108579253
    {'aut_label': '4A', 'centralizer': '6.c1.a1', 'counter': 6, 'group_counter': 25, 'group_order': 120, 'label': '4A', 'order': 4, 'powers': [2, 6, 6], 'representative': 28861, 'size': 6}
  • id: 108579254
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 25, 'group_order': 120, 'label': '5A1', 'order': 5, 'powers': [9, 10, 1], 'representative': 119168, 'size': 1}
  • id: 108579255
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 25, 'group_order': 120, 'label': '5A-1', 'order': 5, 'powers': [10, 9, 1], 'representative': 238336, 'size': 1}
  • id: 108579256
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 25, 'group_order': 120, 'label': '5A2', 'order': 5, 'powers': [8, 7, 1], 'representative': 476672, 'size': 1}
  • id: 108579213
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 25, 'group_order': 120, 'label': '5A-2', 'order': 5, 'powers': [7, 8, 1], 'representative': 59584, 'size': 1}
  • id: 108579214
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 25, 'group_order': 120, 'label': '6A', 'order': 6, 'powers': [5, 2, 11], 'representative': 178772, 'size': 2}
  • id: 108579215
    {'aut_label': '6B1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 25, 'group_order': 120, 'label': '6B1', 'order': 6, 'powers': [5, 3, 13], 'representative': 744801, 'size': 2}
  • id: 108579216
    {'aut_label': '6B1', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 25, 'group_order': 120, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 12], 'representative': 148961, 'size': 2}
  • id: 108579217
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 25, 'group_order': 120, 'label': '10A1', 'order': 10, 'powers': [9, 16, 2], 'representative': 804384, 'size': 1}
  • id: 108579218
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 25, 'group_order': 120, 'label': '10A-1', 'order': 10, 'powers': [10, 17, 2], 'representative': 685216, 'size': 1}
  • id: 108579219
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 25, 'group_order': 120, 'label': '10A3', 'order': 10, 'powers': [7, 15, 2], 'representative': 863968, 'size': 1}
  • id: 108579220
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 25, 'group_order': 120, 'label': '10A-3', 'order': 10, 'powers': [8, 14, 2], 'representative': 446880, 'size': 1}
  • id: 108579221
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 18, 'group_counter': 25, 'group_order': 120, 'label': '10B1', 'order': 10, 'powers': [9, 20, 3], 'representative': 119191, 'size': 2}
  • id: 108579222
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 19, 'group_counter': 25, 'group_order': 120, 'label': '10B-1', 'order': 10, 'powers': [10, 21, 3], 'representative': 238351, 'size': 2}
  • id: 108579224
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 20, 'group_counter': 25, 'group_order': 120, 'label': '10B3', 'order': 10, 'powers': [7, 19, 3], 'representative': 59611, 'size': 2}
  • id: 108579225
    {'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 21, 'group_counter': 25, 'group_order': 120, 'label': '10B-3', 'order': 10, 'powers': [8, 18, 3], 'representative': 476671, 'size': 2}
  • id: 108579226
    {'aut_label': '10C1', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 25, 'group_order': 120, 'label': '10C1', 'order': 10, 'powers': [7, 24, 4], 'representative': 1984, 'size': 6}
  • id: 108579227
    {'aut_label': '10C1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 25, 'group_order': 120, 'label': '10C-1', 'order': 10, 'powers': [8, 25, 4], 'representative': 12586, 'size': 6}
  • id: 108579228
    {'aut_label': '10C1', 'centralizer': '6.b1.a1', 'counter': 24, 'group_counter': 25, 'group_order': 120, 'label': '10C3', 'order': 10, 'powers': [10, 23, 4], 'representative': 7936, 'size': 6}
  • id: 108579229
    {'aut_label': '10C1', 'centralizer': '6.b1.a1', 'counter': 25, 'group_counter': 25, 'group_order': 120, 'label': '10C-3', 'order': 10, 'powers': [9, 22, 4], 'representative': 3968, 'size': 6}
  • id: 108579230
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 25, 'group_order': 120, 'label': '15A1', 'order': 15, 'powers': [28, 9, 5], 'representative': 417083, 'size': 2}
  • id: 108579231
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 25, 'group_order': 120, 'label': '15A-1', 'order': 15, 'powers': [29, 10, 5], 'representative': 595827, 'size': 2}
  • id: 108579232
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 25, 'group_order': 120, 'label': '15A2', 'order': 15, 'powers': [27, 8, 5], 'representative': 297929, 'size': 2}
  • id: 108579233
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 25, 'group_order': 120, 'label': '15A-2', 'order': 15, 'powers': [26, 7, 5], 'representative': 834166, 'size': 2}
  • id: 108579235
    {'aut_label': '20A1', 'centralizer': '6.c1.a1', 'counter': 30, 'group_counter': 25, 'group_order': 120, 'label': '20A1', 'order': 20, 'powers': [14, 32, 6], 'representative': 27931, 'size': 6}
  • id: 108579236
    {'aut_label': '20A1', 'centralizer': '6.c1.a1', 'counter': 31, 'group_counter': 25, 'group_order': 120, 'label': '20A-1', 'order': 20, 'powers': [15, 33, 6], 'representative': 17391, 'size': 6}
  • id: 108579237
    {'aut_label': '20A1', 'centralizer': '6.c1.a1', 'counter': 32, 'group_counter': 25, 'group_order': 120, 'label': '20A3', 'order': 20, 'powers': [16, 31, 6], 'representative': 22351, 'size': 6}
  • id: 108579238
    {'aut_label': '20A1', 'centralizer': '6.c1.a1', 'counter': 33, 'group_counter': 25, 'group_order': 120, 'label': '20A-3', 'order': 20, 'powers': [17, 30, 6], 'representative': 26071, 'size': 6}
  • id: 108579239
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 34, 'group_counter': 25, 'group_order': 120, 'label': '30A1', 'order': 30, 'powers': [26, 14, 11], 'representative': 387286, 'size': 2}
  • id: 108579240
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 35, 'group_counter': 25, 'group_order': 120, 'label': '30A-1', 'order': 30, 'powers': [27, 15, 11], 'representative': 625623, 'size': 2}
  • id: 108579241
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 36, 'group_counter': 25, 'group_order': 120, 'label': '30A7', 'order': 30, 'powers': [28, 17, 11], 'representative': 655419, 'size': 2}
  • id: 108579242
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 37, 'group_counter': 25, 'group_order': 120, 'label': '30A-7', 'order': 30, 'powers': [29, 16, 11], 'representative': 714995, 'size': 2}
  • id: 108579243
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 38, 'group_counter': 25, 'group_order': 120, 'label': '30B1', 'order': 30, 'powers': [26, 18, 12], 'representative': 536241, 'size': 2}
  • id: 108579244
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 39, 'group_counter': 25, 'group_order': 120, 'label': '30B-1', 'order': 30, 'powers': [27, 19, 13], 'representative': 625630, 'size': 2}
  • id: 108579246
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 40, 'group_counter': 25, 'group_order': 120, 'label': '30B7', 'order': 30, 'powers': [28, 21, 12], 'representative': 506456, 'size': 2}
  • id: 108579247
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 41, 'group_counter': 25, 'group_order': 120, 'label': '30B-7', 'order': 30, 'powers': [29, 20, 13], 'representative': 327708, 'size': 2}
  • id: 108579248
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 42, 'group_counter': 25, 'group_order': 120, 'label': '30B11', 'order': 30, 'powers': [26, 18, 13], 'representative': 834161, 'size': 2}
  • id: 108579249
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 43, 'group_counter': 25, 'group_order': 120, 'label': '30B-11', 'order': 30, 'powers': [27, 19, 12], 'representative': 357502, 'size': 2}
  • id: 108579250
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 44, 'group_counter': 25, 'group_order': 120, 'label': '30B13', 'order': 30, 'powers': [29, 20, 12], 'representative': 715004, 'size': 2}
  • id: 108579251
    {'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 45, 'group_counter': 25, 'group_order': 120, 'label': '30B-13', 'order': 30, 'powers': [28, 21, 13], 'representative': 655416, 'size': 2}
• 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: 3929575
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1a', '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], 'schur_index': 1}
  • id: 3929583
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1b', '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], 'schur_index': 1}
  • id: 3929584
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1c', '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], 'schur_index': 1}
  • id: 3929585
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1d', '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], 'schur_index': 1}
  • id: 3929590
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3929576
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 0, 2, 2, 2, 2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0], 'schur_index': 1}
  • id: 3929577
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, 0, 2, 2, 2, 2, -1, 1, 1, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3929586
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1e', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 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], 'schur_index': 1}
  • id: 3929587
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1f', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -1, -1, -1, -1, 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], 'schur_index': 1}
  • id: 3929588
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1g', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 4, -4, -1, -1, -1, -1, 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], 'schur_index': 1}
  • id: 3929589
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 4, -4, -1, -1, -1, -1, 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], 'schur_index': 1}
  • id: 3929578
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2d', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, 0, 4, 4, 4, 4, 2, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0], 'schur_index': 1}
  • id: 3929579
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2e', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 8, 8, 0, -4, 0, -2, -2, -2, -2, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3929580
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2f', 'multiplicity': 4, 'nt': [20, 12], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 0, -2, -2, -2, -2, -8, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0], 'schur_index': 1}
  • id: 3929581
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2g', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, -8, 0, -4, 0, -2, -2, -2, -2, -4, 4, 4, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 3929582
    {'cdim': 2, 'counter': 16, 'faithful': True, 'group': '120.25', 'group_order': 120, 'image': None, 'label': '120.25.2h', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -8, 0, -4, -4, -4, -4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, -2, 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: 5486909
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 120, 'label': '120.25.1a', '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]]]}
  • id: 5486920
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 60, 'label': '120.25.1b', '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]]]}
  • id: 5486931
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 60, 'label': '120.25.1c', '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]]]}
  • id: 5486942
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 60, 'label': '120.25.1d', '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]]]}
  • id: 5486949
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.25.1e1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[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, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]]]}
  • id: 5486950
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.25.1e2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[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, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]]]}
  • id: 5486951
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.25.1e3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[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, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]]]}
  • id: 5486952
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.25.1e4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[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, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]]]}
  • id: 5486953
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 12, 'label': '120.25.1f1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-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, 1]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[1, -1]], [[1, -2]], [[-1, 1]]]}
  • id: 5486910
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 12, 'label': '120.25.1f2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-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, -1]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[1, 1]], [[1, 2]], [[-1, -1]]]}
  • id: 5486911
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 12, 'label': '120.25.1f3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-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, -2]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[1, 2]], [[1, -1]], [[-1, -2]]]}
  • id: 5486912
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 12, 'label': '120.25.1f4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-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, 2]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[1, -2]], [[1, 1]], [[-1, 2]]]}
  • id: 5486913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.25.1g1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-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, 1]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[1, -1]], [[1, -2]], [[-1, 1]]]}
  • id: 5486914
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.25.1g2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-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, -1]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[1, 1]], [[1, 2]], [[-1, -1]]]}
  • id: 5486915
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.25.1g3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-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, -2]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[1, 2]], [[1, -1]], [[-1, -2]]]}
  • id: 5486916
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.25.1g4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-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, 2]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[1, -2]], [[1, 1]], [[-1, 2]]]}
  • id: 5486917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.25.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[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, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]]]}
  • id: 5486918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.25.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[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, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]]]}
  • id: 5486919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.25.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[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, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]]]}
  • id: 5486921
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.25.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[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, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]]]}
  • id: 5486922
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 20, 'label': '120.25.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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: 5486923
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 15, 'label': '120.25.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]]]}
  • id: 5486924
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 10, 'label': '120.25.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5486925
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 5, 'label': '120.25.2d1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]]]}
  • id: 5486926
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 5, 'label': '120.25.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]]]}
  • id: 5486927
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 26, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.25.2e1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -2]], [[2, -1]], [[2, 2]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]]]}
  • id: 5486928
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 27, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.25.2e2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 2]], [[2, 1]], [[2, -2]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]]]}
  • id: 5486929
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 28, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.25.2e3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 2]], [[2, 1]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]]]}
  • id: 5486930
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 29, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.25.2e4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -2]], [[2, -1]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]]]}
  • id: 5486932
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 30, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.25.2f1', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, -2]], [[0, 0]]]}
  • id: 5486933
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 31, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.25.2f2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 2]], [[0, 0]]]}
  • id: 5486934
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 32, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.25.2f3', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[0, 0]], [[0, 0]], [[-2, 2]], [[-2, -1]], [[0, 0]]]}
  • id: 5486935
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 33, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.25.2f4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[0, 0]], [[0, 0]], [[-2, -2]], [[-2, 1]], [[0, 0]]]}
  • id: 5486936
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 34, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.25.2g1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-2, -2]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[-1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, 1]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, -2]], [[1, 1]]]}
  • id: 5486937
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 35, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.25.2g2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, -1]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, 2]], [[1, -1]]]}
  • id: 5486938
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 36, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.25.2g3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 2]], [[-2, 1]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, -1]], [[1, -2]]]}
  • id: 5486939
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 37, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.25.2g4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -2]], [[-2, -1]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, 1]], [[1, 2]]]}
  • id: 5486940
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 38, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h1', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -6]], [[2, 6]], [[2, -3]], [[2, 3]], [[1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[-2, -3]], [[-2, 3]], [[-2, 6]], [[-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, -3]], [[-1, 6]], [[-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[1, 6]], [[-2, 1], [-1, 6]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, 2], [-1, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[1, 3]], [[-1, 2], [1, 7]], [[2, 1], [1, 6]], [[1, -3]], [[1, -6]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]]]}
  • id: 5486941
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 39, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h2', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 6]], [[2, -6]], [[2, 3]], [[2, -3]], [[1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[-2, 3]], [[-2, -3]], [[-2, -6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 3]], [[-1, -6]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-1, 6]], [[1, -6]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[1, 2], [-1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[2, 1], [1, 6]], [[1, -3]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[1, 3]], [[1, 6]], [[-1, 2], [1, 7]]]}
  • id: 5486943
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 40, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -6]], [[2, 6]], [[2, -3]], [[2, 3]], [[1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[-2, -3]], [[-2, 3]], [[-2, 6]], [[-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, -3]], [[-1, 6]], [[-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[1, 6]], [[2, 1], [1, 6]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[-1, 2], [1, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[1, 3]], [[1, 2], [-1, 7]], [[-2, 1], [-1, 6]], [[1, -3]], [[1, -6]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]]]}
  • id: 5486944
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 41, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h4', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 6]], [[2, -6]], [[2, 3]], [[2, -3]], [[1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[-2, 3]], [[-2, -3]], [[-2, -6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -3]], [[-1, 3]], [[-1, -6]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [1, 6]], [[1, -6]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[-1, 2], [1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[-2, 1], [-1, 6]], [[1, -3]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[1, 3]], [[1, 6]], [[1, 2], [-1, 7]]]}
  • id: 5486945
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 42, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h5', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 6]], [[2, -6]], [[1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[-2, 6]], [[-2, -6]], [[-2, 3]], [[-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -6]], [[-1, 6]], [[-1, 3]], [[-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, 7]], [[1, 3]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-2, 1], [-1, 6]], [[1, 2], [-1, 7]], [[1, -6]], [[2, 1], [1, 6]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, 6]], [[1, -3]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]]]}
  • id: 5486946
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 43, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h6', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -6]], [[2, 6]], [[1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[-2, -6]], [[-2, 6]], [[-2, -3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6]], [[-1, -6]], [[-1, -3]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, -3]], [[-1, 2], [1, 7]], [[-2, 1], [-1, 6]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, 6]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[1, 2], [-1, 7]], [[1, -6]], [[1, 3]], [[2, 1], [1, 6]]]}
  • id: 5486947
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 44, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h7', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, -3]], [[2, 3]], [[2, 6]], [[2, -6]], [[1, 0]], [[1, 0], [2, 5]], [[-1, 0], [-2, 5]], [[-2, 6]], [[-2, -6]], [[-2, 3]], [[-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -6]], [[-1, 6]], [[-1, 3]], [[-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [-1, 7]], [[1, 3]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[2, 1], [1, 6]], [[-1, 2], [1, 7]], [[1, -6]], [[-2, 1], [-1, 6]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, 6]], [[1, -3]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]]]}
  • id: 5486948
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 45, 'cyclotomic_n': 15, 'dim': 2, 'faithful': True, 'field': [1, -1, 1], 'group': '120.25', 'group_counter': 25, 'group_order': 120, 'image': None, 'image_isoclass': '120.25', 'image_order': 120, 'indicator': 0, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.25.2h8', 'nt': [60, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 3]], [[2, -3]], [[2, -6]], [[2, 6]], [[1, 0]], [[-1, 0], [-2, 5]], [[1, 0], [2, 5]], [[-2, -6]], [[-2, 6]], [[-2, -3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6]], [[-1, -6]], [[-1, -3]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1], [1, 3], [-2, 4], [2, 5], [-2, 7]], [[1, -3]], [[1, 2], [-1, 7]], [[2, 1], [1, 6]], [[1, 0], [-1, 2], [1, 3], [-2, 4], [1, 6], [-1, 7]], [[-2, 0], [2, 1], [-1, 3], [2, 4], [-2, 5], [2, 7]], [[1, 6]], [[-1, 0], [1, 2], [-1, 3], [2, 4], [-1, 6], [1, 7]], [[-1, 2], [1, 7]], [[1, -6]], [[1, 3]], [[-2, 1], [-1, 6]]]}
• 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: 61328828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 120, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '120.25.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61328839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 60, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 61328850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 60, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.2.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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61328854
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 60, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.2.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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 61328855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 20, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '120.25.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61328856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 30, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.25.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['S', 'C2'], '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: 61328857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 61328858
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.25.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61328859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': True, 'core_order': 24, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '120.25.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61328829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 20, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61328830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.25.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61328831
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 61328832
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 15, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '120.25.8.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': '8.3', '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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 61328833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 12, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 61328834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 12, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61328835
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 12, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 61328836
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 10, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.25.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['Z', 'U1'], '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: 61328837
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 5, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61328838
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 61328840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '120.25.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
  • id: 61328841
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 6, 'counter': 21, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.25.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], '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: 61328842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61328843
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 3, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.25.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 61328844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 5, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '120.25.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', '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: 61328845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.25.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61328846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.25.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61328847
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61328848
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '120.25.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C4'], '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: 61328849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 2, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.25.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], '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: 61328851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 61328852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.25.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 61328853
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.25', 'ambient_counter': 25, 'ambient_order': 120, 'ambient_tex': 'C_{15}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '120.25.120.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': True, 'proper': False, 'quotient': '120.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 61328828
    {'ambient': '120.25', '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': '12.a1.a1', 'complements': ['120.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7480, 6712, 6189, 4769, 6560, 4342, 5160, 4342], 'generators': [893731, 992, 774572, 208557, 744780], 'label': '120.25.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '12.4', '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': '12.4'}
  • id: 61328829
    {'ambient': '120.25', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': ['20.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5817, 1061, 4100, 8808, 5737, 8508, 7251, 8508], 'generators': [893731, 893760, 119168], 'label': '120.25.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '12.4', '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': '2.1'}
  • id: 61328830
    {'ambient': '120.25', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3910, -1, 7243, -1, 2742, -1, 1920, -1], 'generators': [992, 893760, 119168], 'label': '120.25.6.b1.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.b1.a1', 'projective_image': '12.4', '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': '2.1'}
  • id: 61328831
    {'ambient': '120.25', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8178, -1, 9651, -1, 8826, -1, 4567, -1], 'generators': [28861, 893760, 119168], 'label': '120.25.6.c1.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.c1.a1', 'projective_image': '12.4', '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': '2.1'}
  • id: 61328832
    {'ambient': '120.25', 'aut_centralizer_order': 12, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1162, 3594, 1333, 1308, 2325, 6284, 3771, 6284], 'generators': [208557, 744780], 'label': '120.25.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61328833
    {'ambient': '120.25', 'aut_centralizer_order': 24, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': ['12.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '30.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7441, 4868, 3422, 7136, 7124, 4307, 8639, 4307], 'generators': [893731, 774572, 744780], 'label': '120.25.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '60.11', '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': '2.1'}
  • id: 61328834
    {'ambient': '120.25', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': ['12.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '30.b1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6459, 6947, 5253, 3261, 3833, 847, 3012, 847], 'generators': [992, 774572, 744780], 'label': '120.25.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '60.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61328835
    {'ambient': '120.25', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': ['12.b1.a1', '12.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.c1.a1'], 'core': '10.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9538, 8147, 9253, 4619, 9658, 2295, 5400, 2295], 'generators': [28861, 774572, 744780], 'label': '120.25.10.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.a1', 'normal_contained_in': ['2.c1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '60.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61328836
    {'ambient': '120.25', 'aut_centralizer_order': 24, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 24, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4268, 2116, 6815, 5696, 5377, 7838, 4586, 7838], 'generators': [893760, 119168], 'label': '120.25.12.a1.a1', 'mobius_quo': 1, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328837
    {'ambient': '120.25', 'aut_centralizer_order': 12, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '60.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2531, -1, 398, -1, 3139, -1, 7492, -1], 'generators': [893731, 119168], 'label': '120.25.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328838
    {'ambient': '120.25', 'aut_centralizer_order': 4, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 24, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '60.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [566, -1, 3055, -1, 846, -1, 1532, -1], 'generators': [992, 119168], 'label': '120.25.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '24.8', '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': '1.1'}
  • id: 61328839
    {'ambient': '120.25', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 6, 'centralizer': '2.a1.a1', 'complements': ['60.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6129, 3594, 3472, 7285, 5173, 8720, 7409, 8720], 'generators': [893731, 774572, 208557, 744780], 'label': '120.25.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '12.4', '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': '2.1'}
  • id: 61328840
    {'ambient': '120.25', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8253, -1, 8239, -1, 8086, -1, 6159, -1], 'generators': [893731, 992, 893760], 'label': '120.25.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '60.11', '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': '4.2'}
  • id: 61328841
    {'ambient': '120.25', 'aut_centralizer_order': 48, 'aut_label': '20.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '60.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6705, 5981, 5801, 3494, 6116, 3424, 5326, 3424], 'generators': [774572, 744780], 'label': '120.25.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61328842
    {'ambient': '120.25', 'aut_centralizer_order': 24, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3342, -1, 756, -1, 3879, -1, 8445, -1], 'generators': [893731, 744780], 'label': '120.25.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328843
    {'ambient': '120.25', 'aut_centralizer_order': 8, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.b1.a1'], 'contains': ['40.a1.a1', '60.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2286, -1, 3084, -1, 1586, -1, 2272, -1], 'generators': [992, 744780], 'label': '120.25.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61328844
    {'ambient': '120.25', 'aut_centralizer_order': 24, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 24, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [255, 3346, 1950, 4156, 2547, 6284, 3994, 6284], 'generators': [119168], 'label': '120.25.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.8', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.8', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328845
    {'ambient': '120.25', 'aut_centralizer_order': 48, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': ['4.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5581, 3024, 4388, 7136, 6828, 4784, 6705, 4784], 'generators': [893731, 893760], 'label': '120.25.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61328846
    {'ambient': '120.25', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4447, -1, 7312, -1, 4591, -1, 2985, -1], 'generators': [992, 893760], 'label': '120.25.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '60.11', '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': '2.1'}
  • id: 61328847
    {'ambient': '120.25', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8593, -1, 8924, -1, 8455, -1, 5993, -1], 'generators': [28861, 893760], 'label': '120.25.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '60.11', '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': '2.1'}
  • id: 61328848
    {'ambient': '120.25', 'aut_centralizer_order': 48, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2220, 4708, 2139, 3246, 3213, 3619, 4660, 3619], 'generators': [744780], 'label': '120.25.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '120.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61328849
    {'ambient': '120.25', 'aut_centralizer_order': 96, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5251, 3067, 6178, 5381, 5747, 4890, 5326, 4890], 'generators': [893760], 'label': '120.25.60.a1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328850
    {'ambient': '120.25', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.35', 'aut_weyl_index': 2, 'centralizer': '12.a1.a1', 'complements': ['60.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '6.b1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4589, 5981, 5104, 1192, 3666, 2895, 2226, 2895], 'generators': [992, 774572, 208557, 744780], 'label': '120.25.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '12.4', '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': '12.4'}
  • id: 61328851
    {'ambient': '120.25', 'aut_centralizer_order': 48, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3182, -1, 756, -1, 3879, -1, 7094, -1], 'generators': [893731], 'label': '120.25.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '120.25', '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': '1.1'}
  • id: 61328852
    {'ambient': '120.25', 'aut_centralizer_order': 16, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 96, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.b1.a1'], 'contains': ['120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1558, -1, 3253, -1, 1734, -1, 2633, -1], 'generators': [992], 'label': '120.25.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '120.25', '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': '1.1'}
  • id: 61328853
    {'ambient': '120.25', 'aut_centralizer_order': None, 'aut_label': '120.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': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1'], 'contains': [], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2220, 3902, 2139, 4156, 3213, 4890, 4660, 4890], 'generators': [], 'label': '120.25.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328854
    {'ambient': '120.25', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.35', 'aut_weyl_index': 2, 'centralizer': '12.a1.a1', 'complements': ['60.b1.a1', '60.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8442, 8939, 9572, 3924, 8826, 5808, 3753, 5808], 'generators': [28861, 774572, 208557, 744780], 'label': '120.25.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '12.4', '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': '12.4'}
  • id: 61328855
    {'ambient': '120.25', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7611, -1, 7820, -1, 6560, -1, 5160, -1], 'generators': [893731, 992, 893760, 119168], 'label': '120.25.3.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': '12.4', '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': '4.2'}
  • id: 61328856
    {'ambient': '120.25', 'aut_centralizer_order': 12, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4779, 5688, 5104, 2732, 4572, 6284, 3753, 6284], 'generators': [774572, 208557, 744780], 'label': '120.25.4.a1.a1', 'mobius_quo': -1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61328857
    {'ambient': '120.25', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '20.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2418, -1, 349, -1, 1577, -1, 9676, -1], 'generators': [893731, 208557, 744780], 'label': '120.25.4.b1.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.b1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61328858
    {'ambient': '120.25', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.5', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '20.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [623, -1, 1473, -1, 541, -1, 541, -1], 'generators': [992, 208557, 744780], 'label': '120.25.4.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.c1.a1', 'projective_image': '24.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61328859
    {'ambient': '120.25', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': ['24.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9745, 7650, 6239, 5712, 7623, 653, 6224, 653], 'generators': [893731, 992, 774572, 744780], 'label': '120.25.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}