Irreducible (2,3,7)-subgroups of PGLn(F), n⩽7, II

The paper presents further results towards the complete classification of the Hurwitz subgroups of PGL7(F), where F is an algebraically closed field of characteristic p⩾0. We classify up to conjugation all non-rigid triples (x,y,xy)∈GLn(F) such that x2=y3=7(xy)=1, and 〈x,y〉 is an irreducible subgroup of GLn(F). Moreover, for any such triple we find the minimal field of definition of 〈x,y〉.