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?



The simple groups with an absolutely irreducible projective representations with small degrees
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.


