[*a repost from SE due to the lack of response*]

Given a group $G$, let $A$ be a $G$-module and let $N\trianglelefteq G$. If I understand it correctly, the superscript "G/N" in the third term of the standard inflation-restriction exact sequence $$ 0\to H^1(G/N,A^N)\to H^1(G,A)\to H^1(N,A)^{G/N}\to H^2(G/N,A^N)\to H^2(G,A) $$ means the fixed points under the action of $G/N$ on the first cohomology group $H^1(N,A)$. But how is this action defined? Is there an elementary definition (in terms of cocycles) that does not refer to the Lyndon–Hochschild–Serre spectral sequence?

Cohomology of Groups! $\endgroup$