Spectral sets in ${\mathbb{Z}}_{p^{2}qr}$ tile

We prove the every spectral set in ${\mathbb{Z}}_{p^{2}qr}$ tiles, where $p$, $q$ and $r$ are primes. Combining this with a recent result of Malikiosis we obtain that Fuglede’s conjecture holds for ${\mathbb{Z}}_{p^{2}qr}$.