GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
1
prime 7
class 3
generators {a, b}
relations {b^7, a^7 = [b, a, b], (a * b * [b, a, b] )^7,
[b, a, a, a, a, b, a] = 1}
;
2
Standard
20
6
1 0 0 0
0 1 0 1
1 3 0 0
0 1 0 0
6 0 0 0
0 1 0 0
3 0 0 0
0 1 0 0
1 2 0 0
0 6 0 0
1 4 0 0
0 4 0 0
1
0