[GAP Forum] conjugacy classes of finite matrix groups with prescribed order

[Bill Allombert]

Dear GAP forum,

I have finite matrix groups, for example
G:=Group([[0, 0, 0, 2, -1, 1, 1, -3], [0, 0, 0, -1, 1, 0, 0, 1], [0, 0, 0,
1, 0, 0, 0, -2], [0, 0, 0, 1, -1, 1, 1, -2], [0, 0, 0, 1, -1, 0, 1, -1],
[0, 0, 1, 0, 0, 0, 0, -1], [0, 1, 0, 1, 0, 0, 0, -1], [1, -1, -1, 0, -1,
0, 0, -1]], [[-5, 0, 0, 2, 1, 4, 4, 4], [1, 0, 0,
-1, 0, -1, 0, 0], [-2, 0, 0, 1, 0, 2, 1, 2], [-3, 0, 0, 1, 1, 3, 2, 2],
[-2, 0, 0, 1, 0, 2, 2, 1], [-1, 0, 0, 0, 0, 1, 1, 1], [-2, 1, 1,
1, 1, 1, 1, 1], [-1, -1, 0, 0, 0, 1, 1, 1]]);
I need to compute the conjugacy classes of elements of order 4 and/or
with minimal polynomial x^2+1.

Of course I can do
Filtered(ConjugacyClasses(G), g->Order(Representative(g))=4);
or
Filtered(ConjugacyClasses(G), g->Representative(g)^2=-IdentityMat(8));
but I have thousands of such groups so any suggestion to speed up the
process is welcome.

Maybe there is a way to compute only conjugacy classes of the right
order ?

Cheers,
Bill.