What will be the group if the groups given by following descriptions were represented using symbols/notation (like $Z_p$ etc.)
1). Cyclic group of order $p^2 q$.
2). Semidirect product of cyclic group of order $q$ by a cyclic group of order $p^2$, where the action by conjugation of a generator is an automorphism of order $p$.
3). Semidirect product of cyclic group of order $q$ by a cyclic group of order $p^2$, where the action by conjugation of a generator is an automorphism of order $p^2$.
4). Semidirect product of cyclic group of order $pq$ by a cyclic group of order $p$, where the action by conjugation of a generator is an automorphism of order $p$.
5). Direct product of cyclic group of order $p$ and cyclic group of order $pq$, which is also same as direct product of elementary abelian group of order $p^2$ and cyclic group of order $q$.
Please help me with this question.
Thanks a lot in advance.
Cyclic groups of order $n$ are often denoted multiplicatively by $C_n$. For $n=p,p^2,p^2q$ and so on we write $C_p,C_{p^2},C_{p^2q}$. The semidirect product then is denoted by $$ C_q\rtimes_{\theta}C_{p^2}. $$ Here the automorphism is denoted by $\theta$.