GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
1
prime 2
class 2
generators {a, b}
relations {a^4, b^2 = [b, a, b], b = a^2 * b^-1 * a^2} ;
2
Standard
9
3
1 0 0 1
0 1 0 0
1 0 0 0
0 1 0 1
1 1 1 0
0 1 1 1
1 #soluble
0