## Cohomology of $SO(p,q,\mathbb{Z})$ with p=3,q=19

I would like to understand the topology of the moduli space of Einstein orbifold metrics on the $$K3$$-surface. It is known that this space is given by the bi-quotient $$SO(3,19;\mathbb{Z})\setminus SO(3,19)/SO(3)\times SO(19)$$ and I know that this has the same rational cohomology as $$SO(3,19;\mathbb{Z})$$. Is there anything known about these groups? Unfortunately my knowledge on arithmetic groups is very limited.