(i) Give the definition of a $p$-Sylow subgroup of a group.

(ii) Let $G$ be a group of order $2835=3^{4} \cdot 5 \cdot 7$. Show that there are at most two possibilities for the number of 3-Sylow subgroups, and give the possible numbers of 3-Sylow subgroups.

(iii) Continuing with a group $G$ of order 2835 , show that $G$ is not simple.