A cohomological property of p-groups

Let p be a prime, script G sign a finite p-group, Heng hooktop sign any finite group with order divisible by p, and α : script G sign → Aut(Heng hooktop sign) any action of script G sign on Heng hooktop sign. We show that the cardinality of the set of all derivations d : script G sign → Heng hooktop sign with respect to this action is a multiple of p. This generalises theorems of Frobenius and Hall.