Let $\displaystyle G$ be a group of order $\displaystyle 3825$. Prove that if $\displaystyle H$ is a normal subgroup of order $\displaystyle 17$ in $\displaystyle G$ then $\displaystyle H \leq Z(G)$, where $\displaystyle Z(G)$ represents the center of $\displaystyle G$.

(Please do not use sylow's or cauchy's theorems.)