GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap4r8 / pkg / carat / carat-2.1b1 / tables / qcatalog / dim5 / dir.2-2;2-2;1 / ordnung.288 / (1)^5(3)^4 / group.556
561086 views#g5 5 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 -1 5 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 1 5 1 1 0 0 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 1 0 0 0 0 0 0 1 5 1 1 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 5 1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 1 2^5 * 3^2 = 288 % order of the group