GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
5 3 1 prime 5 class 1 generators {a, b, c, d} relations { (a * b^d ) = 1, (c * d^a) = 1, [c, a, a] = 1, [c, b, b, a] }; 2 Standard 5 2 4 1 4 0 2 0 0 1 0 0
GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
5 3 1 prime 5 class 1 generators {a, b, c, d} relations { (a * b^d ) = 1, (c * d^a) = 1, [c, a, a] = 1, [c, b, b, a] }; 2 Standard 5 2 4 1 4 0 2 0 0 1 0 0