Finite Permutation Groups

sage.categories.finite_permutation_groups.FinitePermutationGroups

The category of finite permutation groups, i.e. groups concretely represented as groups of permutations acting on a finite set.

It is currently assumed that any finite permutation group comes endowed with a distinguished finite set of generators (method group_generators); this is the case for all the existing implementations in Sage.

EXAMPLES:

sage: C = PermutationGroups().Finite(); C
Category of finite enumerated permutation groups
sage: C.super_categories()
[Category of permutation groups,
 Category of finite groups,
 Category of finite finitely generated semigroups]

sage: C.example()
Dihedral group of order 6 as a permutation group