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This question is based on a question when is the restriction $H^2(G,\mathbb{C}^*)\to H^2(K,\mathbb{C}^*)$ surjective? I am asking this as a new question as I already asked that user but got no response.

I wish to know what is that algorithm by which I can check that a 2-cocycle on $K$ is image of 2-cocycle on some some subgroup of $G$ under the restriction map.

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    $\begingroup$ You can do this in Magma (see here) in the case when the module is a finitely generated abelian group. That does not apply to ${\mathbb C}^*$ but I think you could still get the result by using a suitable finitely generated subgroup of ${\mathbb C}^*$ (you probably just need the $|G|$th roots of unity). $\endgroup$
    – Derek Holt
    Commented Dec 18, 2015 at 12:24

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