GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#2-generator exponent 5 groups
1 #set up group presentation
c5c5
5
1
1
{a, b}
{}
0
7 #compute its 5-covering group
9 #enter p-group generation
1 #supply automorphisms
2 #number of automorphisms
2 0
0 1
4 1
4 0
0 #number of soluble automorphisms
5 #iteration option
5 #class bound
1 #all descendants?
0 #order bound?
0 #PAG-generating sequence
0 #default algorithm?
0 #rank of initial segment
0 #process terminal descendants completely
5 #exponent law to enforce
0 #metabelian law to enforce
1 #default output
0 #exit
0 #exit