  We consider a subclass of the class of group-theoretical fusion categories:
To every finite group $G$ and subgroup $H$ one can associate the category of
$G$-graded vector spaces with a two-sided $H$-action compatible with the
grading. We derive a formula that computes higher Frobenius-Schur indicators
for the objects in such a category using the combinatorics and representation
theory of the groups involved in their construction. We calculate some explicit
examples for inclusions of symmetric groups.
