  In this article, we study two different types of operators, the localization
operator and Weyl transform, on the reduced Heisenberg group with
multidimensional center $\mathcal{G}$. The group $\mathcal{G}$ is a quotient
group of non-isotropic Heisenberg group with multidimensional center
$\mathcal{H}^m$ by its center subgroup. Firstly, we define the localization
operator using a wavelet transform on $\mathcal{G}$ and obtain the product
formula for the localization operators.
  Next, we define the Weyl transform associated to the Wigner transform on
$\mathcal{G}$ with the operator-valued symbol. Finally, we have shown that the
Weyl transform is not only a bounded operator but also a compact operator when
the operator-valued symbol is in $L^p,1\leq p\leq 2,$ and it is an unbounded
operator when $p>2$.
