GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g2 f1 z1 c1 5x 5 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5x 5 -1 0 0 0 1 0 0 0 0 1 0 -1 0 0 1 0 0 -1 0 1 0 0 0 -1 1 5x 5 5 -1 -1 -1 -1 -1 5 -1 -1 -1 -1 -1 5 -1 -1 -1 -1 -1 5 -1 -1 -1 -1 -1 5 5d0 % zentr -1 5d0 % cen -1 2^5 * 3^2 * 5^1 = 1440 %order of the group