GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g2 f2 z2 n1 c2 4x 4 0 0 0 -1 0 0 1 0 1 0 0 0 0 1 0 0 4x 4 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 4x 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 4x 4 0 0 1 -1 0 0 1 1 1 1 0 0 -1 1 0 0 4d0 % zentr -1 4x0 % zentr 1 0 1 1 1 1 -1 1 0 1 4 % additional normalizer 0 0 0 -1 0 0 -1 0 0 1 0 0 1 0 0 0 4d0 % cen -1 4x0 % cen 1 0 1 1 1 1 -1 1 0 1 2^4 = 16 %order of the group