[GAP Forum] Certain Subgroups of SL(3, q) of Order q^3 for small q

[Sandeep Murthy]

Hello,

If G = SL(3,q), the special linear group over the finite field F_q, then
I am interested in the following subgroups:

S = { set of all upper triangular matrices in G with 1s on the diagonal, and elements x,y,z above the diagonal},
T = { set of all lower triangular matrices in G with 1s on the diagonal, and elements x,y,z below the diagonal}.

How can I define these subgroups in GAP for specific small values of q, like 2, 3, 4 etc.?

Sincerely, Sandeep.