Group algebra of nonstandard symmetric groups broken

[darij]

I have found and recorded the problem in #16926, although it predates said ticket. Quoting src/sage/groups/perm_gps/permgroup_named.py:

    def algebra(self, base_ring):
        """
        Return the symmetric group algebra associated to ``self``.

        .. WARNING::

            This is broken!

                sage: S = SymmetricGroup([2,3,5])
                sage: S.an_element()
                (2,3,5)
                sage: S.algebra(QQ)(_)
                Traceback (most recent call last):
                ...
                ValueError: The permutation has length 3 but its maximal element is 5. Some
                 element may be repeated, or an element is missing, but there is something
                 wrong with its length.

            Best make it a usual group algebra with none of the bells and whistles
            of the SGA but with functioning methods.

        EXAMPLES::

            sage: S4 = SymmetricGroup(4)
            sage: S4.algebra(QQ)
            Symmetric group algebra of order 4 over Rational Field
        """
        from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra
        return SymmetricGroupAlgebra(base_ring, self)

[nthiery]

I just implemented that in #16926; this ticket can probably be closed as duplicate.

[darij]

Great job! Can I ask you to review my doctests? (probably half a minute of work, thanks!)

[tscrim]

Done.