Formats: - HTML - YAML - JSON - 2026-07-27T19:25:28.966092
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 5], 'aut_gens': [[1, 4], [1, 12], [5, 4]], 'aut_group': '20.3', 'aut_hash': 3, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20, 'aut_permdeg': 5, 'aut_perms': [18, 34], 'aut_phi_ratio': 2.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [4, 5, 1, 2], [5, 4, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '20.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': False, 'autcentquo_order': 20, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5', 'cc_stats': [[1, 1, 1], [2, 5, 1], [4, 5, 2], [5, 4, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '20.3', 'commutator_count': 1, 'commutator_label': '5.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [4, 5, 2, 1], [5, 4, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 20, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[4, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '20.3', 'hash': 3, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [4, 5], 'inner_gens': [[1, 12], [13, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 20, 'inner_split': True, 'inner_tex': 'F_5', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [4, 1]], 'label': '20.3', 'linC_count': 1, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'F5', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 5, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 14, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 5], [4, 10], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1]], 'representations': {'PC': {'code': 2551363, 'gens': [1, 3], 'pres': [3, -2, -2, -5, 6, 110, 77]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [23561683, 28172809]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33, 10], 'family': 'AGL'}, {'d': 1, 'q': 5, 'gens': [33, 10], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 127]}, 'Perm': {'d': 5, 'gens': [10, 23, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'F_5', 'transitive_degree': 5, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 109174482
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3, 'group_order': 20, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 109174483
      {'aut_label': '2A', 'centralizer': '5.a1.a1', 'counter': 2, 'group_counter': 3, 'group_order': 20, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 14, 'size': 5}
    • id: 109174484
      {'aut_label': '4A1', 'centralizer': '5.a1.a1', 'counter': 3, 'group_counter': 3, 'group_order': 20, 'label': '4A1', 'order': 4, 'powers': [2, 3], 'representative': 7, 'size': 5}
    • id: 109174485
      {'aut_label': '4A-1', 'centralizer': '5.a1.a1', 'counter': 4, 'group_counter': 3, 'group_order': 20, 'label': '4A-1', 'order': 4, 'powers': [2, 4], 'representative': 9, 'size': 5}
    • id: 109174486
      {'aut_label': '5A', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 3, 'group_order': 20, 'label': '5A', 'order': 5, 'powers': [5, 1], 'representative': 4, 'size': 4}
  • gps_qchar • Show schema
    • id: 4171502
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '20.3', 'group_order': 20, 'image': None, 'label': '20.3.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 4171503
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '20.3', 'group_order': 20, 'image': None, 'label': '20.3.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1], 'schur_index': 1}
    • id: 4171504
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '20.3', 'group_order': 20, 'image': None, 'label': '20.3.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2], 'schur_index': 1}
    • id: 4171505
      {'cdim': 4, 'counter': 4, 'faithful': True, 'group': '20.3', 'group_order': 20, 'image': None, 'label': '20.3.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 0, 0, 0, -1], 'schur_index': 1}
  • gps_char • Show schema
    • id: 6082179
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 20, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20.3', 'group_counter': 3, 'group_order': 20, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 20, 'label': '20.3.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 6082180
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 20, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20.3', 'group_counter': 3, 'group_order': 20, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 10, 'label': '20.3.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
    • id: 6082181
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 20, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '20.3', 'group_counter': 3, 'group_order': 20, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 5, 'label': '20.3.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]]]}
    • id: 6082182
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 20, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '20.3', 'group_counter': 3, 'group_order': 20, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 5, 'label': '20.3.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]]]}
    • id: 6082183
      {'center': '20.a1.a1', 'center_index': 20, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 1, 'dim': 4, 'faithful': True, 'field': [0, 1], 'group': '20.3', 'group_counter': 3, 'group_order': 20, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 1, 'label': '20.3.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • gps_subgroup_search • Show schema
    • id: 63654262
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 20, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '20.3.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
    • id: 63654263
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 10, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '20.3.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
    • id: 63654264
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 5, 'counter': 3, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '20.3.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, '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': True, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], '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: 63654265
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '20.3.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 2}
    • id: 63654266
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20.3.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.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': 10, '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: 63654267
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20.3', 'ambient_counter': 3, 'ambient_order': 20, 'ambient_tex': 'F_5', 'central': True, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 1, 'counter': 6, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '20.3.20.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': True, 'proper': False, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C3'], '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: 63654262
      {'ambient': '20.3', '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': '20.a1.a1', 'complements': ['20.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3293, 5000, 3293, 5000, 5000, 5000, 5000, 5000], 'generators': [1, 4, 2], 'label': '20.3.1.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': '20.3', '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': '20.3'}
    • id: 63654263
      {'ambient': '20.3', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5000, 5000, 5000, 5000, 7857, 5000, 7857, 5000], 'generators': [2, 4], 'label': '20.3.2.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': '20.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
    • id: 63654264
      {'ambient': '20.3', 'aut_centralizer_order': 5, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 5, 'centralizer': '4.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8354, 5000, 8354, 5000, 7857, 5000, 7857, 5000], 'generators': [4], 'label': '20.3.4.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '20.3', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 63654265
      {'ambient': '20.3', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1.1', 'aut_weyl_index': 20, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': '5T3', 'count': 5, 'diagramx': [1646, -1, 1646, -1, 2143, -1, 2143, -1], 'generators': [1], 'label': '20.3.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '20.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 63654266
      {'ambient': '20.3', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1.1', 'aut_weyl_index': 20, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': '10T4', 'count': 5, 'diagramx': [5000, -1, 5000, -1, 2143, -1, 2143, -1], 'generators': [2], 'label': '20.3.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '20.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 63654267
      {'ambient': '20.3', 'aut_centralizer_order': None, 'aut_label': '20.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': ['4.a1.a1', '10.a1.a1'], 'contains': [], 'core': '20.a1.a1', 'coset_action_label': '20T5', 'count': 1, 'diagramx': [7500, 5000, 7500, 5000, 5000, 5000, 5000, 5000], 'generators': [], 'label': '20.3.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '20.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}