Formats: - HTML - YAML - JSON - 2026-09-21T01:57:25.461632
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '32.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 8, 'aut_gen_orders': [2, 8], 'aut_gens': [[1], [31], [5]], 'aut_group': '16.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 10, 'aut_perms': [387218, 10692], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1], [16, 1, 8, 1], [32, 1, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_8', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 8, 'autcent_group': '16.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_8', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [8, 1, 4], [16, 1, 8], [32, 1, 16]], 'center_label': '32.1', 'center_order': 32, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1], [16, 1, 8, 1], [32, 1, 16, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 32, 'exponents_of_order': [5], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 16]], 'familial': True, 'frattini_label': '16.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 2, 'irrep_stats': [[1, 32]], 'label': '32.1', 'linC_count': 16, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 16, 'linQ_dim_count': 1, 'linR_count': 8, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C32', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 32, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 1], [4, 2], [8, 4], [16, 8], [32, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 8], 'outer_gen_pows': [0, 0], 'outer_gens': [[31], [5]], 'outer_group': '16.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 10, 'outer_perms': [387218, 10692], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_8', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [32], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1], [8, 1], [16, 1]], 'representations': {'PC': {'code': 572653583, 'gens': [1], 'pres': [5, -2, -2, -2, -2, -2, 10, 26, 42, 58]}, 'GLFp': {'d': 2, 'p': 17, 'gens': [3111]}, 'Perm': {'d': 32, 'gens': [263121961682809333227690318495744000, 127165970120440293996769393998336000, 59187974339659933956082255161332976, 25199055155429228508133415361942982, 8231691320578226211046411712681647]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [32], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{32}', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 109737945
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 32, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
    • id: 109737956
      {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 32, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
    • id: 109737967
      {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 32, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 8, 'size': 1}
    • id: 109737971
      {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 32, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 24, 'size': 1}
    • id: 109737972
      {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 32, 'label': '8A1', 'order': 8, 'powers': [3], 'representative': 4, 'size': 1}
    • id: 109737973
      {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 32, 'label': '8A-1', 'order': 8, 'powers': [4], 'representative': 28, 'size': 1}
    • id: 109737974
      {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 32, 'label': '8A3', 'order': 8, 'powers': [4], 'representative': 12, 'size': 1}
    • id: 109737975
      {'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 32, 'label': '8A-3', 'order': 8, 'powers': [3], 'representative': 20, 'size': 1}
    • id: 109737976
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 32, 'label': '16A1', 'order': 16, 'powers': [5], 'representative': 2, 'size': 1}
    • id: 109737946
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 32, 'label': '16A-1', 'order': 16, 'powers': [6], 'representative': 30, 'size': 1}
    • id: 109737947
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 32, 'label': '16A3', 'order': 16, 'powers': [7], 'representative': 6, 'size': 1}
    • id: 109737948
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 32, 'label': '16A-3', 'order': 16, 'powers': [8], 'representative': 26, 'size': 1}
    • id: 109737949
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 32, 'label': '16A5', 'order': 16, 'powers': [8], 'representative': 10, 'size': 1}
    • id: 109737950
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 32, 'label': '16A-5', 'order': 16, 'powers': [7], 'representative': 22, 'size': 1}
    • id: 109737951
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 32, 'label': '16A7', 'order': 16, 'powers': [6], 'representative': 14, 'size': 1}
    • id: 109737952
      {'aut_label': '16A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 32, 'label': '16A-7', 'order': 16, 'powers': [5], 'representative': 18, 'size': 1}
    • id: 109737953
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 32, 'label': '32A1', 'order': 32, 'powers': [9], 'representative': 1, 'size': 1}
    • id: 109737954
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 32, 'label': '32A-1', 'order': 32, 'powers': [10], 'representative': 31, 'size': 1}
    • id: 109737955
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 32, 'label': '32A3', 'order': 32, 'powers': [11], 'representative': 3, 'size': 1}
    • id: 109737957
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 32, 'label': '32A-3', 'order': 32, 'powers': [12], 'representative': 29, 'size': 1}
    • id: 109737958
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 32, 'label': '32A5', 'order': 32, 'powers': [13], 'representative': 5, 'size': 1}
    • id: 109737959
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 32, 'label': '32A-5', 'order': 32, 'powers': [14], 'representative': 27, 'size': 1}
    • id: 109737960
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 32, 'label': '32A7', 'order': 32, 'powers': [15], 'representative': 7, 'size': 1}
    • id: 109737961
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 32, 'label': '32A-7', 'order': 32, 'powers': [16], 'representative': 25, 'size': 1}
    • id: 109737962
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 1, 'group_order': 32, 'label': '32A9', 'order': 32, 'powers': [16], 'representative': 9, 'size': 1}
    • id: 109737963
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 1, 'group_order': 32, 'label': '32A-9', 'order': 32, 'powers': [15], 'representative': 23, 'size': 1}
    • id: 109737964
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 1, 'group_order': 32, 'label': '32A11', 'order': 32, 'powers': [14], 'representative': 11, 'size': 1}
    • id: 109737965
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 1, 'group_order': 32, 'label': '32A-11', 'order': 32, 'powers': [13], 'representative': 21, 'size': 1}
    • id: 109737966
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 29, 'group_counter': 1, 'group_order': 32, 'label': '32A13', 'order': 32, 'powers': [12], 'representative': 13, 'size': 1}
    • id: 109737968
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 30, 'group_counter': 1, 'group_order': 32, 'label': '32A-13', 'order': 32, 'powers': [11], 'representative': 19, 'size': 1}
    • id: 109737969
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 31, 'group_counter': 1, 'group_order': 32, 'label': '32A15', 'order': 32, 'powers': [10], 'representative': 15, 'size': 1}
    • id: 109737970
      {'aut_label': '32A1', 'centralizer': '1.a1.a1', 'counter': 32, 'group_counter': 1, 'group_order': 32, 'label': '32A-15', 'order': 32, 'powers': [9], 'representative': 17, 'size': 1}
  • gps_qchar • Show schema
    • id: 4381483
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 4381484
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 4381485
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 4381486
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1d', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 4381487
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1e', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 4381488
      {'cdim': 1, 'counter': 6, 'faithful': True, 'group': '32.1', 'group_order': 32, 'image': None, 'label': '32.1.1f', 'multiplicity': 16, 'nt': [32, 33], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 6645583
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 32, 'label': '32.1.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 6645594
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 16, 'label': '32.1.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 6645605
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 8, 'label': '32.1.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
    • id: 6645609
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 8, 'label': '32.1.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
    • id: 6645610
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 5, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 4, 'label': '32.1.1d1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]]]}
    • id: 6645611
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 6, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 4, 'label': '32.1.1d2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]]]}
    • id: 6645612
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 4, 'label': '32.1.1d3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]]]}
    • id: 6645613
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 8, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.a1.a1', 'kernel_order': 4, 'label': '32.1.1d4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]]]}
    • id: 6645614
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e1', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[-1, 3]], [[1, 5]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[-1, 5]], [[1, 3]], [[1, 3]], [[-1, 5]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[1, 5]], [[-1, 3]]]}
    • id: 6645584
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e2', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[1, 5]], [[-1, 3]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 7]], [[1, 3]], [[-1, 5]], [[-1, 5]], [[1, 3]], [[1, 7]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[-1, 3]], [[1, 5]]]}
    • id: 6645585
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e3', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 3]], [[-1, 5]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[1, 5]], [[-1, 3]], [[-1, 3]], [[1, 5]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[-1, 5]], [[1, 3]]]}
    • id: 6645586
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e4', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[-1, 5]], [[1, 3]], [[1, 7]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[-1, 3]], [[1, 5]], [[1, 5]], [[-1, 3]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 7]], [[1, 3]], [[-1, 5]]]}
    • id: 6645587
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e5', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[1, 7]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 7]], [[-1, 7]], [[1, 1]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 7]]]}
    • id: 6645588
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e6', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 3]], [[-1, 7]], [[1, 1]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 3]], [[1, 7]], [[-1, 1]]]}
    • id: 6645589
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e7', 'nt': [16, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 7]], [[1, 1]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 7]], [[1, 7]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 7]]]}
    • id: 6645590
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 16, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '16.1', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.1.1e8', 'nt': [16, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 3]], [[1, 7]], [[-1, 1]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 3]], [[-1, 7]], [[1, 1]]]}
    • id: 6645591
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f1', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 4]], [[-1, 12]], [[-1, 6]], [[1, 10]], [[1, 2]], [[-1, 14]], [[1, 14]], [[-1, 2]], [[-1, 10]], [[1, 6]], [[1, 11]], [[-1, 5]], [[1, 1]], [[-1, 15]], [[-1, 7]], [[1, 9]], [[1, 13]], [[-1, 3]], [[1, 3]], [[-1, 13]], [[-1, 9]], [[1, 7]], [[1, 15]], [[-1, 1]], [[1, 5]], [[-1, 11]]]}
    • id: 6645601
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f10', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[1, 4]], [[-1, 12]], [[1, 12]], [[-1, 4]], [[-1, 2]], [[1, 14]], [[-1, 6]], [[1, 10]], [[-1, 10]], [[1, 6]], [[-1, 14]], [[1, 2]], [[1, 9]], [[-1, 7]], [[-1, 11]], [[1, 5]], [[1, 13]], [[-1, 3]], [[-1, 15]], [[1, 1]], [[-1, 1]], [[1, 15]], [[1, 3]], [[-1, 13]], [[-1, 5]], [[1, 11]], [[1, 7]], [[-1, 9]]]}
    • id: 6645602
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 27, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f11', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[-1, 12]], [[1, 4]], [[-1, 4]], [[1, 12]], [[1, 14]], [[-1, 2]], [[1, 10]], [[-1, 6]], [[1, 6]], [[-1, 10]], [[1, 2]], [[-1, 14]], [[1, 7]], [[-1, 9]], [[-1, 5]], [[1, 11]], [[1, 3]], [[-1, 13]], [[-1, 1]], [[1, 15]], [[-1, 15]], [[1, 1]], [[1, 13]], [[-1, 3]], [[-1, 11]], [[1, 5]], [[1, 9]], [[-1, 7]]]}
    • id: 6645603
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 28, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f12', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[1, 4]], [[-1, 12]], [[1, 12]], [[-1, 4]], [[-1, 2]], [[1, 14]], [[-1, 6]], [[1, 10]], [[-1, 10]], [[1, 6]], [[-1, 14]], [[1, 2]], [[-1, 9]], [[1, 7]], [[1, 11]], [[-1, 5]], [[-1, 13]], [[1, 3]], [[1, 15]], [[-1, 1]], [[1, 1]], [[-1, 15]], [[-1, 3]], [[1, 13]], [[1, 5]], [[-1, 11]], [[-1, 7]], [[1, 9]]]}
    • id: 6645604
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 29, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f13', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[-1, 12]], [[1, 4]], [[-1, 4]], [[1, 12]], [[-1, 14]], [[1, 2]], [[-1, 10]], [[1, 6]], [[-1, 6]], [[1, 10]], [[-1, 2]], [[1, 14]], [[1, 15]], [[-1, 1]], [[1, 13]], [[-1, 3]], [[1, 11]], [[-1, 5]], [[1, 9]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 5]], [[-1, 11]], [[1, 3]], [[-1, 13]], [[1, 1]], [[-1, 15]]]}
    • id: 6645606
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 30, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f14', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[1, 4]], [[-1, 12]], [[1, 12]], [[-1, 4]], [[1, 2]], [[-1, 14]], [[1, 6]], [[-1, 10]], [[1, 10]], [[-1, 6]], [[1, 14]], [[-1, 2]], [[-1, 1]], [[1, 15]], [[-1, 3]], [[1, 13]], [[-1, 5]], [[1, 11]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 7]], [[-1, 11]], [[1, 5]], [[-1, 13]], [[1, 3]], [[-1, 15]], [[1, 1]]]}
    • id: 6645607
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 31, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f15', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[-1, 12]], [[1, 4]], [[-1, 4]], [[1, 12]], [[-1, 14]], [[1, 2]], [[-1, 10]], [[1, 6]], [[-1, 6]], [[1, 10]], [[-1, 2]], [[1, 14]], [[-1, 15]], [[1, 1]], [[-1, 13]], [[1, 3]], [[-1, 11]], [[1, 5]], [[-1, 9]], [[1, 7]], [[-1, 7]], [[1, 9]], [[-1, 5]], [[1, 11]], [[-1, 3]], [[1, 13]], [[-1, 1]], [[1, 15]]]}
    • id: 6645608
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 32, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f16', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[1, 4]], [[-1, 12]], [[1, 12]], [[-1, 4]], [[1, 2]], [[-1, 14]], [[1, 6]], [[-1, 10]], [[1, 10]], [[-1, 6]], [[1, 14]], [[-1, 2]], [[1, 1]], [[-1, 15]], [[1, 3]], [[-1, 13]], [[1, 5]], [[-1, 11]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 7]], [[1, 11]], [[-1, 5]], [[1, 13]], [[-1, 3]], [[1, 15]], [[-1, 1]]]}
    • id: 6645592
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f2', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 12]], [[-1, 12]], [[1, 4]], [[1, 10]], [[-1, 6]], [[-1, 14]], [[1, 2]], [[-1, 2]], [[1, 14]], [[1, 6]], [[-1, 10]], [[-1, 5]], [[1, 11]], [[-1, 15]], [[1, 1]], [[1, 9]], [[-1, 7]], [[-1, 3]], [[1, 13]], [[-1, 13]], [[1, 3]], [[1, 7]], [[-1, 9]], [[-1, 1]], [[1, 15]], [[-1, 11]], [[1, 5]]]}
    • id: 6645593
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f3', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 4]], [[-1, 12]], [[-1, 6]], [[1, 10]], [[1, 2]], [[-1, 14]], [[1, 14]], [[-1, 2]], [[-1, 10]], [[1, 6]], [[-1, 11]], [[1, 5]], [[-1, 1]], [[1, 15]], [[1, 7]], [[-1, 9]], [[-1, 13]], [[1, 3]], [[-1, 3]], [[1, 13]], [[1, 9]], [[-1, 7]], [[-1, 15]], [[1, 1]], [[-1, 5]], [[1, 11]]]}
    • id: 6645595
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f4', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 12]], [[-1, 12]], [[1, 4]], [[1, 10]], [[-1, 6]], [[-1, 14]], [[1, 2]], [[-1, 2]], [[1, 14]], [[1, 6]], [[-1, 10]], [[1, 5]], [[-1, 11]], [[1, 15]], [[-1, 1]], [[-1, 9]], [[1, 7]], [[1, 3]], [[-1, 13]], [[1, 13]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[1, 1]], [[-1, 15]], [[1, 11]], [[-1, 5]]]}
    • id: 6645596
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f5', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 4]], [[-1, 12]], [[1, 6]], [[-1, 10]], [[-1, 2]], [[1, 14]], [[-1, 14]], [[1, 2]], [[1, 10]], [[-1, 6]], [[-1, 3]], [[1, 13]], [[-1, 9]], [[1, 7]], [[-1, 15]], [[1, 1]], [[1, 5]], [[-1, 11]], [[1, 11]], [[-1, 5]], [[-1, 1]], [[1, 15]], [[-1, 7]], [[1, 9]], [[-1, 13]], [[1, 3]]]}
    • id: 6645597
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f6', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 12]], [[-1, 12]], [[1, 4]], [[-1, 10]], [[1, 6]], [[1, 14]], [[-1, 2]], [[1, 2]], [[-1, 14]], [[-1, 6]], [[1, 10]], [[1, 13]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[1, 1]], [[-1, 15]], [[-1, 11]], [[1, 5]], [[-1, 5]], [[1, 11]], [[1, 15]], [[-1, 1]], [[1, 9]], [[-1, 7]], [[1, 3]], [[-1, 13]]]}
    • id: 6645598
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f7', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 4]], [[-1, 12]], [[1, 6]], [[-1, 10]], [[-1, 2]], [[1, 14]], [[-1, 14]], [[1, 2]], [[1, 10]], [[-1, 6]], [[1, 3]], [[-1, 13]], [[1, 9]], [[-1, 7]], [[1, 15]], [[-1, 1]], [[-1, 5]], [[1, 11]], [[-1, 11]], [[1, 5]], [[1, 1]], [[-1, 15]], [[1, 7]], [[-1, 9]], [[1, 13]], [[-1, 3]]]}
    • id: 6645599
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f8', 'nt': [32, 16], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 12]], [[-1, 12]], [[1, 4]], [[-1, 10]], [[1, 6]], [[1, 14]], [[-1, 2]], [[1, 2]], [[-1, 14]], [[-1, 6]], [[1, 10]], [[-1, 13]], [[1, 3]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[1, 15]], [[1, 11]], [[-1, 5]], [[1, 5]], [[-1, 11]], [[-1, 15]], [[1, 1]], [[-1, 9]], [[1, 7]], [[-1, 3]], [[1, 13]]]}
    • id: 6645600
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 25, 'cyclotomic_n': 32, 'dim': 1, 'faithful': True, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '32.1', 'group_counter': 1, 'group_order': 32, 'image': None, 'image_isoclass': '32.1', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 1, 'label': '32.1.1f9', 'nt': [32, 33], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 8]], [[-1, 12]], [[1, 4]], [[-1, 4]], [[1, 12]], [[1, 14]], [[-1, 2]], [[1, 10]], [[-1, 6]], [[1, 6]], [[-1, 10]], [[1, 2]], [[-1, 14]], [[-1, 7]], [[1, 9]], [[1, 5]], [[-1, 11]], [[-1, 3]], [[1, 13]], [[1, 1]], [[-1, 15]], [[1, 15]], [[-1, 1]], [[-1, 13]], [[1, 3]], [[1, 11]], [[-1, 5]], [[-1, 9]], [[1, 7]]]}
  • gps_subgroup_search • Show schema
    • id: 65316213
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 1, 'cyclic': True, 'direct': True, 'hall': 2, 'label': '32.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.1', 'subgroup_hash': 1, 'subgroup_order': 32, 'subgroup_tex': 'C_{32}', 'supersolvable': True, 'sylow': 2}
    • id: 65316214
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 2, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.1.2.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': ['Phi', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
    • id: 65316215
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 3, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.1.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
    • id: 65316216
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.1.8.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': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
    • id: 65316217
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 2, 'counter': 5, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.1.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
    • id: 65316218
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.1', 'ambient_counter': 1, 'ambient_order': 32, 'ambient_tex': 'C_{32}', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 1, 'counter': 6, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '32.1.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '32.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{32}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', '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 • Show schema
    • id: 65316213
      {'ambient': '32.1', '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': '1.a1.a1', 'complements': ['32.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [1], 'label': '32.1.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1.1', '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': '1.1'}
    • id: 65316214
      {'ambient': '32.1', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [2], 'label': '32.1.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '2.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 65316215
      {'ambient': '32.1', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [4], 'label': '32.1.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '4.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 65316216
      {'ambient': '32.1', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [8], 'label': '32.1.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '8.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 65316217
      {'ambient': '32.1', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 16, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [16], 'label': '32.1.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '16.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.1', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 65316218
      {'ambient': '32.1', 'aut_centralizer_order': None, 'aut_label': '32.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': ['16.a1.a1'], 'contains': [], 'core': '32.a1.a1', 'coset_action_label': '32T33', 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000], 'generators': [], 'label': '32.1.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}