Let $G$ be a finite group with trivial action on $k^\times$$\mathbb C^\times$. And given a 2-cocycle $\alpha$ in its Schur multiplier group $H^2(G,k^\times)$$H^2(G,\mathbb C^\times)$, as an explicit map from $G\times G\to k^\times$$G\times G\to \mathbb C^\times$. I am wondering if there is an algorithm to determine if $\alpha$ is $0$ in $H^2(G,k^\times)$$H^2(G,\mathbb C^\times)$? I vaguely remember there is such an algorithm mentioned in some paper but cannot find it now. Also I am wondering if there is such an implementation in software like GAP or Magma.
Edit: I want to work with $k=\mathbb C$.