  In this paper we investigate the Fuglede's conjecture for
$\mathbb{Z}_{p^2q^2r}$ and provide a proof of it under the condition $p^2q^2
\le r$. We develop a new technique by studying the divisibility of the mask
polynomial of a given set by some system of cyclotomic polynomials. This
combined with a so-called mod-p-method gives a strong tool to study Fuglede's
conjecture in this and some other cases.
