Explicit formulas are derived for the number of isomorphism classes of Beauville surfaces with non-abelian metacyclic p-groups or nilpotency class 2 p-groups.
Fairbairn, Beauvillep-groups: A Survey, in Groups St Andrews 2017 in Birming- ham, editors C
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The Number of Isomorphism Classes of Beauville Surfaces with Beauville $p$-Group
Explicit formulas are derived for the number of isomorphism classes of Beauville surfaces with non-abelian metacyclic p-groups or nilpotency class 2 p-groups.