Scott's formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in PGLn(F) for n≤7 which are Hurwitz, where F is an algebraically closed field. For the groups G2(q), q≥5, and the Janko groups J1 and J2 it provides explicit (2,3,7)-generators.