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  • Allen Knutson, the GL(n,q) number of conjugacy classes is a polynomial in q which you can work out by explicitly computing the number of conjugacy classes of each type; here is the GL(3,q) case: groupprops.subwiki.org/wiki/??? For SL, PGL, PSL, we do not get polynomials but PORC functions; the statement for SL, for instance, is here: groupprops.subwiki.org/wiki/???
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