A Note on Beauville p-Groups

Abstract

We examine which p-groups of order ⩽p 6 are Beauville. We completely classify them for groups of order ⩽p 4. We also show that the proportion of 2-generated groups of order p 5 that are Beauville tends to 1 as p tends to infinity; this is not true, however, for groups of order p 6. For each prime p we determine the smallest nonabelian Beauville p-group.