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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)
I have found and recorded the problem in #16926, although it predates said ticket. Quoting src/sage/groups/perm_gps/permgroup_named.py:
Depends on #16926
CC: @sagetrac-sage-combinat @tscrim @avirmaux @nthiery
Component: combinatorics
Keywords: symmetric group, group algebra, permutations
Reviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/18005
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