I am referring specifically to this example http://planetmath.org/groupsoforderpq
In Case 2, the group should be $\mathbb{Z}_q\rtimes\mathbb{Z}_p$.
How do we write it in the presentation of $$G=\langle a,b\mid a^{p}=b^{q}=1,aba^{-1}=b^{i_{0}}\rangle?$$
Thanks for help.
I am thinking of something in the directions of internal semidirect product, but not sure exactly how.