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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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1
prime 7 
class 3 
generators {a, b}
relations {a^7, b^7 = [b, a, a], [b, a, b, b, b, b, b] = 1}
;

2
Standard
10

7

1 0 0 0 1
0 1 0 0 0

1 0 0 0 0
0 1 0 1 0 

1 0 0 0 0
0 1 0 0 1

1 0 0 0 0 
6 1 0 0 0 

6 0 0 0 0 
2 1 0 0 0 

6 0 0 0 0 
0 6 0 0 0 

6 0 0 0 0 
4 5 0 0 0 

1

0