:1,7,1,Group([(1,2,4,3,6,7,5)])
:2,14,5,Group([(2,5)(3,6)(4,7),(1,2,4,3,6,7,5)])
:3,21,4,Group([(2,4,6)(3,5,7),(1,2,4,3,6,7,5)])
:4,42,4,Group([(2,3,4,5,6,7),(1,2,4,3,6,7,5)])
:5,168,11,L3,2 on projective points.1
:6,2520,11,AlternatingGroup([1..7])
:7,5040,0,SymmetricGroup([1..7])
