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