I am wondering about how to take the group $G(m,p,n)$ as input in GAP. The groups $G(m,p,n)$ appear in the classification of unitary reflection groups. The group $G(1,1,n)$ is the symmetric group $S_n$. Further, the group $G(m,1,n)$ is the group $C_m\wr S_n$, where $C_m$ is the cyclic group of order $m$. I was thinking if there is a direct way I can take these groups as input by specifying values of $m,p,n$. These groups $G(m,p,n)$ are certain semidirect products of the group $A(m,p,n)$ with $S_n$ where,
$$A(m,p,n):=\{(\theta_1,\theta_2,\ldots,\theta_n)\in \mu_m^n\mid (\theta_1\theta_2\cdots \theta_n)^{m/p}=1\}.$$
Here, $\mu_m$ is the group of $m^{th}$ roots of unity and $\mu_m^n=\underbrace{\mu_m\times \cdots \times \mu_m}_{n\;times}$. Thanks in advance for any kind of suggestions.