:1,5,1,Group([(1,2,3,5,4)])
:2,10,5,Group([(2,4)(3,5),(1,2,3,5,4)])
:3,20,4,Group([(2,3,4,5),(1,2,3,5,4)])
:4,60,11,AlternatingGroup([1..5])
:5,120,0,SymmetricGroup([1..5])
