Slender partial quadrangles and their automorphisms

The partial quadrangle $PQ(s,t,\mu)$ is an incidence system consisting of points and lines in which every line contains $s+1$ points, every point sits on $t+1$ lines (two lines meet in at most one point), and the meet of the neighborhoods of any two non-adjacent points in the collinearity graph is a $\mu$-coclique. We provide a classification for partial quadrangles $PQ(s,t,\mu)$ with $t\leqslant 6$, and study into their automorphisms.