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.4-2;1 / ordnung.576 / (1)^9(3)^8 / max.12
561052 views#g4 5 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 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 0 1 0 0 0 0 0 -1 5 -1 -1 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 1 2^6 * 3^2 = 576 % order of the group