GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g2 f5 n8 % 1-th homogenously dec. group, 1 zclass 5 % generator 1 -1 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 -1 5 % generator 0 -1 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5d1 % invariant form 0 0 0 1 0 5x0 % invariant form 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 5d1 % invariant form 0 0 0 0 1 5d1 % invariant form 0 0 1 0 0 5x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 5d0 % generator of normalizer -1 5x0 % generator of normalizer 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 -1 5 % generator of normalizer -1 0 0 0 0 -1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5 % generator of normalizer 1 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5 % generator of normalizer 0 1 0 0 0 -1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5 % generator of normalizer 1 -1 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 1 2 0 0 0 0 -1 5 % generator of normalizer 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 -1 5 % generator of normalizer -1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 1 1 2^1 * 3^1 = 6 % order of the group