  For a finite group $G$, the representation dimension is the smallest integer
realizable as the degree of a complex faithful representation of $G$. In this
article, we compute representation dimension for some $p$-groups, their direct
products, and groups with certain conditions on nonlinear irreducible
characters. We also make similar computations for the smallest integer
realizable as the degree of an irreducible complex faithful representation of
$G$, if one exists. In the appendix, we present GAP codes to compute these
numbers.
