Generalized Quadrangles Derived from Groups and Having \(s=t+2\)

The known generalized quadrangles with parameters \((s,t)\) where \(|s-t| = 2\) have been characterized in several ways by M. De Soete \([D]\), M. De Soete and J. A. Thas \([DT1]\), \([DT2]\), \([DT4]\), and the present author \([P]\). Certain of these results are interpreted for a coset geometry construction.