  The Star graph $S_n$ is the Cayley graph of the symmetric group $Sym_n$ with
the generating set $\{(1\mbox{ }i): 2\leq i\leq n \}$.
  Arumugam and Kala proved that $\{\pi\in Sym_n: \pi(1)=1\}$ is a perfect code
in $S_n$ for any $n, n\geq 3$. In this note we show that for any $n, n\geq 6$
the Star graph $S_n$ contains a perfect code which is a union of cosets of the
embedding of $PGL(2,5)$ into $Sym_6$.
