12.58 (1992)

A generalized quadrangle $GQ(s, t)$ with parameters $s, t$ is by definition an incidence system consisting of points and lines in which every line consists of $s + 1$ points, every two different lines have at most one common point, each point belongs to $t + 1$ lines, and for any point $a$ not lying on a line $L$ there is a unique line containing $a$ and intersecting $L$.
$\qquad$ a) Does $GQ(4, 11)$ exist?
$\qquad$ b) Can the automorphism group of a hypothetical $GQ(5, 7)$ contain involutions?