[GAP Forum] Conjugacy classes of involutions in SU(n, q) and SO(n, q)

[Max Horn]

Dear GAP forum,

is there an efficient way in GAP to get a list of (representatives of)
conjugacy classes of involutions in SU(n,q) and SO(n,q)? Specifically for
n=4, 5,6, and at least up to q <= 9.

Right now, I use this rather crude code:
invs := Filtered(List(ConjugacyClasses(G),Representative), x->Order(x)=2);;

Sadly, it works for me only up to q=4. And takes far too long, too ;).

Alternatively, could somebody point out a good reference to me where I can
find descriptions of the conjugacy classes of involutions in said groups,
which I could use to implement relevant code myself? The atlas helps me
only so far, since I would like to do this for bigger values of q, too.

Thanks as always for you generous help,
Max