On unit group of finite semisimple group algebras of non-metabelian groups of order 108

In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ non-metabelian order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ $108$ but only $4$ them non-metabelian. We consider all find Wedderburn decomposition their algebras. And as by-product obtain groups.