GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g3 f1 z1 c1 4x 4 0 1 0 0 -1 1 0 0 0 0 1 0 0 0 0 1 4x 4 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 4x 4 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 4x 4 2 -1 0 0 -1 2 0 0 0 0 2 -1 0 0 -1 2 4d0 % zentr -1 4d0 % cen -1 2^5 * 3^2 = 288%order of the group