Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1-9-6, 1-35-28, 1-135-120$.

Is there a formular for the orbit sizes in general? Thank you.