Lifting a 5-dimensional representation of $M_{11}$ to a complex unitary representation of a certain amalgam

Abstract

We lift the $5$-dimensional characteristic $3$ representation of $M_{11}$ to a complex representation of the amalgam $\mathrm{GL}(2,3){\ast }_{D_8}{S}_4$, and consider its reduction (mod $p$) for other odd primes.