We lift the $5$-dimensional characteristic $3$ representation of $M_{11}$ to a complex representation of the amalgam ${rm GL}(2,3)*_{D_8}S_{4}$, and consider its reduction (mod $p$) for other odd primes.
We consider an amalgam of groups constructed from fusion systems for different odd primes p and q. This amalgam contains a self-normalizing cyclic subgroup of order pq and isolated elements of order p and q.
In this paper we study finite p-solvable groups having irreducible complex characters chi in Irr(G) which take roots of unity values on the p-singular elements of G.
