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