Strong Gelfand Pairs of the Symplectic Group ${\mathrm{Sp}}_4(q)$ where $q$ is even

Abstract

A strong Gelfand pair $(G,H)$ is a finite group $G$ together with a subgroup $H$ such that every irreducible character of $H$ induces to a multiplicity-free character of $G$. We classify the strong Gelfand pairs of the finite symplectic groups ${\mathrm{Sp}}_4(q)$ for even $q$.