  It is shown that a Cayley multigraph over a group $G$ with generating
multiset $S$ is integral (i.e., all of its eigenvalues are integers) if $S$
lies in the integral cone over the boolean algebra generated by the normal
subgroups of $G$. The converse holds in the case when $G$ is abelian. This in
particular gives an alternative, character theoretic proof of a theorem of
Bridges and Mena (1982). We extend this result to provide a necessary and
sufficient condition for a Cayley multigraph over a Hamiltonian group to be
integral, in terms of character sums and the structure of the generating set.
