GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g3 f1 z1 c1 4x 4 -1 0 0 0 0 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 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 4x 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 4d0 % zentr -1 4d0 % cen -1 2^7 * 3^1 = 384 %order of the group