I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics. (Sufficiently applied mathematics such as cryptography, coding theory, or statistics still count.)
Let me clarify: I am not interested in applications of elementary group theory which happen to involve finite groups (e.g. cyclic/dihedral/easy groups as molecular symmetries). I am interested in applications of topics specifically coming from finite group theory as a discipline, like one might see in Isaacs, Huppert, or Robinson.
"The Schur multiplier has order 2640, so we should point the laser that way."
"Is this computer system secure?" "No - Frobenius kernels are nilpotent."
I'm aware of this MO post, but many of the applications listed there are inside mathematics or fall in the "applications of easy groups" category. It is entirely possible that what I'm looking for doesn't exist, and that finite group theory is still an untouchable, pure subject, like number theory in the days of G. H. Hardy. But perhaps not. Does anyone know of any applications of the higher level stuff?