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Ideally I would like to know the Schur multiplier of $Gl(n, F_3)$, but perhaps this is not reasonable to ask. But for a small fixed $n$, this should be known, but i could not find any result when doing a google search. Could someone kindly provide a reference for the same? Thanks.

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According to this paper (which I just found with a Google search, so it'd probably be useful to look up the citation it lists), the Schur multiplier of $GL_n(\mathbb{F}_p)$ is trivial for $p\not = 2$. The paper mentions that it was "computed only recently" (the paper it lists was published in 2008), though that might just be the general case rather than $p = 3$ specifically.

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  • $\begingroup$ The Schur Multipliers of the finite simple groups have all been known for along time, and it is not hard to go from ${\rm SL}(n,p)$ to ${\rm GL}(n,p)$. You are right, it is trivial except when $p=2$ and $n=3$ or $4$. $\endgroup$ – Derek Holt Jul 25 '14 at 21:22
  • $\begingroup$ Ah, thanks. In fact, even Wikipedia has a list of the Schur multipliers for the finite simple groups. $\endgroup$ – anomaly Jul 25 '14 at 21:24

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