GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g2 f5 n21 % 1-th homogenously dec. group, 4 zclass 5 % generator -1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 -1 -1 0 0 1 0 1 0 5 % generator 1 0 0 0 0 0 1 -1 0 -1 0 0 0 0 -1 0 -1 0 0 1 0 1 0 1 0 5d1 % invariant form 1 0 0 0 0 5x0 % invariant form 0 0 0 0 1 0 0 1 0 0 0 0 0 -1 0 5x0 % invariant form 0 1 0 -1 0 0 -1 0 0 0 -1 0 0 0 0 5x0 % invariant form 0 0 0 0 0 0 0 1 -1 0 0 1 -1 0 0 5x0 % invariant form 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 5d0 % generator of normalizer -1 5 % generator of normalizer -1 0 0 0 0 0 -1 0 0 1 0 -1 0 -1 0 0 1 -1 0 -1 0 0 0 0 1 5 % generator of normalizer 1 0 0 0 0 0 1 -1 0 -1 0 0 0 0 -1 0 0 1 1 1 0 0 -1 0 0 5 % generator of normalizer 1 0 0 0 0 0 0 -1 -1 0 0 -1 0 -1 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 -1 -1 0 0 1 0 1 0 1 0 5 % generator of normalizer -1 -1 1 1 1 0 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 0 0 1 1 1 0 0 1 0 0 0 0 -1 -1 0 0 1 0 1 0 5 % generator of normalizer 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 -1 0 0 1 0 1 0 1 0 5 % generator of normalizer -1 0 0 0 0 1 0 -1 -1 0 0 -1 0 -1 0 -1 0 0 1 0 0 0 0 0 1 5x0 % generator of normalizer -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 5 % generator of normalizer 1 0 0 0 0 0 1 -1 0 -1 0 0 0 0 -1 0 -1 0 0 1 0 1 0 1 0 5 % generator of normalizer -1 -2 2 2 2 0 1 0 0 0 0 0 1 0 0 0 -1 0 0 1 0 1 0 1 0 5 % generator of normalizer 1 0 0 0 0 0 0 -1 -1 0 0 -1 0 -1 0 0 0 1 1 1 0 0 -1 0 0 5 % generator of normalizer -1 -2 2 2 2 0 0 -1 -1 0 0 -1 0 -1 0 0 0 0 1 0 0 0 0 0 1 5 % generator of normalizer 1 1 -1 -1 -1 0 0 0 1 0 0 0 0 0 -1 0 0 -1 -1 0 0 1 0 1 0 5 % generator of normalizer 1 1 -1 -1 -1 0 -1 0 0 1 0 -1 0 -1 0 0 1 0 0 0 0 0 -1 0 0 5 % generator of normalizer 1 1 -1 -1 -1 0 -1 0 0 1 0 -1 0 -1 0 0 1 -1 0 -1 0 0 0 0 1 5 % generator of normalizer 1 2 -2 -2 -2 0 0 1 1 1 0 0 1 0 0 0 0 -1 -1 0 0 1 0 1 0 5 % generator of normalizer 1 1 -1 -1 -1 0 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 -1 0 0 5 % generator of normalizer 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 -1 -1 0 0 1 0 1 0 5 % generator of normalizer -1 0 0 0 0 0 -1 0 0 1 0 -1 0 -1 0 0 1 0 0 0 0 0 -1 0 0 2^1 * 3^1 = 6 % order of the group