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

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#start point for Nottingham group 

1
Nott
5
3
1
{a, b}
{a^5, b^5, [b, a, b]}
0

7        #compute 5-covering group

2
Nott

9

1
6
1 0 0 0
0 1 0 1

1 1 0 0
0 1 0 0

1 0 0 0 
0 4 0 0 

1 0 0 0
0 2 0 0 

4 0 0 0 
0 1 0 0 

2 0 0 0 
0 1 0 0 

0         #number of soluble automorphisms

5         #iteration 
4         #class bound
0         #construct all descendants?
1         #step size  
1         #PAG-generating sequence 

0         #default algorithm?
4         #rank of subgroup
0         #space efficient?
0         #completely process terminal descendants?
0         #exponent law
0         #metabelian law 

1         #default output 

0         
0