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For a complex algebraic variety $X$, we show that triviality of the sheafcohomology group $H^0(X,\mathcal{H}^3)$ occurring on the second page of theBloch-Ogus spectral sequence follows from a condition on the integral Chowgroup $CH^2X$ and the integral cohomology group $H^3(X, Z)$. In the case that$X$ is an appropriate approximation to the classifying stack $BG$ of a finite$p$-group $G$, this result states that the group $G$ has no degree threecohomological invariants. As a corollary we show that the nonabelian groups oforder $p^3$ for odd prime $p$ have no degree three cohomological invariants.

Vanishing of Degree 3 Cohomological Invariants