Petersen graph is not a Cayley graph [duplicate]

Let $ P\simeq Cay(G,S)$, then $|S|=3$ and $|G|=10$, then $G\simeq \mathbb{C_{10}}$ or $\mathbb{D_{10}}$, in both cases $G$ has cycle order 4, whereas $P$ has cycle of or 5.