Irreducible (2,3,7)-subgroups of , n 7

Let be an algebraically closed field of characteristic p 0. For n 7 we classify (up to multiplication by scalar matrices) the similarity invariants of the triples such that x2, y3 and (xy)7 are scalar, and x,y is an irreducible subgroup of . Moreover, for those triples which are rigid, we determine the isomorphism type of the projective image of x,y , provided p>0. This leads to the discovery of new Hurwitz groups and gives a significant contribution to the classification of the Hurwitz subgroups of , n 7, which is our final goal.