Integral representations of metacyclic groups over a local field

Let G be a group generated by two elements α and β such that α^t = 1. Then the commutator of G, $δ = αβα−1β−1$ commutes with α and β where δ^t = 1 and t = p^m Furthermore, G is known as an integral representation over a local field. In this paper, the integral representations of metacyclic groups over a local field are determined.