frobenius group

[mona123]

Let $\displaystyle p$ be a prime number. We define the frobenius group by

$\displaystyle F_{p(p-1}=\left\{\begin{pmatrix}a&b\\0&1\end{pmatrix}, a\in \mathbb{F}_p^{\times}, b\in \mathbb{F}_p\right\}$


I want to identify the center $\displaystyle Z(F_{p(p-1)})$ and $\displaystyle F'_{p(p-1)}=[F_{p(p-1)}:F_{p(p-1)}]$

with I will be gratefull if you could help me.