  The Hochschild cohomology ring of a group algebra is an object that has
received recent attention, but is difficult to compute, in even the simplest of
cases. In this paper, we use the product formula due to Witherspoon and Siegel
to extend some of their computations. In particular, we compute the Hochschild
cohomology algebra of group algebras kG where |G| is less than 16, and we
provide an alternative computation of the ring $HH^*(k(E \ltimes P))$
considered by Kessar and Linckelmann.
