Constructing a Representation of the Group (2, 3, 7; 11)

We construct a representation of the finitely presented groupG :=«x, y x2, y2, (xy)7,[x,y]11». This is done by lifting a representation over a finite field to a sufficently large quotient of local field and by finding minimal polynomials for the entries of this representation. We finally obtain a 7-dimensional representation over an algebraic number fieldKof degree 10 over the rationals, providing a homomorphism ofGinto a Lie group of typeG2overK.