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In the question "Simple Hurwitz Groups of order less than 10^7", it came up that all the Hurwitz groups with absolutely irreducible projective representations of degrees up to 7 over any field are determined (This later turned out to be false).

I was wondering, exactly what are all the simple groups with absolutely irreducible projective representations of degrees up to 7 over any field? Also, for which of those classes of groups is it determined which ones are hurwitz groups?

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    $\begingroup$ The published tables of Hiss and Malle (coprime characteristic) and Lubeck (defining characteristic) contain complete classifications up to dimension $250$. $\endgroup$
    – Derek Holt
    Commented Feb 8, 2015 at 12:31
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    $\begingroup$ Concerning which ones are Hurwitz groups, I don't think you are going to get any more information than was in the answers and comments to your previous question. It is all in the literature. $\endgroup$
    – Derek Holt
    Commented Feb 8, 2015 at 12:33

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The references for the low-dimensional projective representations of quasisimple groups are:

G. Hiss and G. Malle, `Low dimensional representations of quasi-simple groups', LMS J. Comput. Math. 4 (2001) 22-63. [Corrigenda: LMS J. Comput. Math. 5 (2002) 95-126].

F. Lübeck, `Small degree representations of finite Chevalley groups in defining characteristic', LMS J. Comput. Math. 4 (2001) 135-169.

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    $\begingroup$ Note that the 2002 paper by Hiss-Malle contains a complete corrected list. The journal is freely available here: journals.cambridge.org/action/displayIssue?iid=6564372 $\endgroup$
    – Jim Humphreys
    Commented Feb 8, 2015 at 15:08
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    $\begingroup$ Well it's complete apart from a few generic cases like ${\rm (P)SL}(2,q)$. Fortunately the LMS JCM is open access. $\endgroup$
    – Derek Holt
    Commented Feb 8, 2015 at 16:58

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