 Transgression in group cohomology

The transgression $d_2:H^1(H,M{)}^Q\to H^2(Q,M^H)$ is the first differential crossing from the vertical to the horizontal edge of the Lyndon–Hochschild–Serre spectral sequence. If a representative on $H$ is extended to a cochain on $G$, its coboundary descends to the representing two-cocycle on $Q$.