We show that the set of natural numbers which are dimensions of irreducible complex representations of finite quasisimple groups (excluding the natural representations of alternating groups) has density zero. We also determine the exact asymptotics for this set, showing that it has (7 + o(1))x/ log x elements less than x. Our tools combine representation theory and number theory. An application to finite subgroups of classical Lie groups is given.
Bibliographical noteFunding Information:
The second author acknowledges the support of an EPSRC Visiting Fellowship at Imperial College London, and a grant from the Israel Science Foundation.