# Revision history [back]

Sage's built-in help is useful here.

sage: PermutationGroup?
Definition:     PermutationGroup(gens=None, gap_group=None, domain=None, canonicalize=True, category=None)
Docstring:
Return the permutation group associated to x (typically a list of
generators).

INPUT:

* "gens" - list of generators (default: "None")

* "gap_group" - a gap permutation group (default: "None")

* "canonicalize" - bool (default: "True"); if "True", sort
generators and remove duplicates

OUTPUT:

* A permutation group.


So indeed you get a permutation group, with these things as generators. You can't multiply groups.

A similar look at help will show you that Permutation does not give an element of a group, though you can convert an element of such a group to one.

But you can get group elements from your group. Try this.

sage: G = SymmetricGroup(4)
sage: G([(1,2)])
(1,2)
sage: G([(1,2)])*G([(1,3)])*G([(1,4)])
(1,2,3,4)