Representation Dimension of Some Finite Groups

For a finite group G, the representation dimension is the minimal degree of a complex faithful representation of G. In this article, we compute representation dimension for some finite p-groups, in particular, for all p-groups of order up to p 5 , their direct products, and groups with certain conditions on nonlinear irreducible characters. We also compute the minimal degree of a complex faithful irreducible representation of such groups, if one exists. In the appendix, we present GAP codes to compute these numbers.