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The so-called "local-global" conjectures in the representation theory offinite groups relate the representation theory of $G$ to that of certain propersubgroups, such as the normalizers of particular $p$-groups. Recent results byseveral authors reduce some of these conjectures to showing that a certaincollection of stronger conditions holds for all finite simple groups. Here, weshow that $G=Sp_6(2^a)$ is "good" for these reductions for the McKayconjecture, the Alperin weight conjecture, and their blockwise versions.

$Sp_6(2^a)$ is "Good" for the McKay, Alperin Weight, and Related Local-Global Conjectures