Assume F is a finite field of order pf and q is an odd prime for which pf-1=sqm, where m≥1 and (s,q)=1. In this article, we obtain the order of the symmetric and the unitary subgroup of the semisimple group algebra FCq. Further, for the extension G of Cq=⟨b⟩ by an abelian group A of order pn with CA(b)={e}, we prove that if m>1, or (s+1)≥q and 2n≥f(q-1), then G does not have a normal complement in V(FG).