GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g3 f1 6x6 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 -1 0 0 1 0 0 0 -1 0 0 1 6x6 0 0 0 1 0 0 0 0 0 -1 -1 -1 0 0 0 0 1 0 1 0 0 0 0 0 -1 -1 -1 0 0 0 0 1 0 0 0 0 6x6 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 6x6 4 2 2 -2 -1 -1 2 4 2 -1 -2 -1 2 2 4 -1 -1 -2 -2 -1 -1 4 2 2 -1 -2 -1 2 4 2 -1 -1 -2 2 2 4 2^5 * 3^2 = 288 dim6/6-2d