Thread: Find the subspaces and show a linear transformation permutes subspace

Let be a vector space over a field finite field K, in which |K| = 4. Show that V has exactly five 1-dimensional subspaces, say and that a non-singular linear transformation of V permutes these five subspaces.

Also, the question goes on to "associate to the map in (where is the symmetric group of 5 elements under composition).

This seems very unclear to me - what does it actually mean? I've got to show that the map defines a monomorphism from SL(2,4) into which I think would be manageable provided I understood what was meant by the "corresponding permutation" in the first place!