Let $E=(\mathbb{Z}/p\mathbb{Z})^n$, an elementary Abelian p-group. Let $k$ be an algebraically closed field of characteristic 0. There is a good description of $H^*(E,F^{\times})$ where $F$ is a field of characteristic $p$ Is there a description of $H^*(E,k^{\times})$ where $k$ is a field of characteristic 0? The goal is to describe $H^3(E,k^{\times})$ as an $Aut(E)\cong GL_n(\mathbb{F}_p)$-module.