The alternating groups and K3 surfaces

In this note, we consider all possible extensions GG of a non-trivial perfect group HH acting faithfully on a K3K3 surface XX. The pair (X,G)(X,G) is proved to be uniquely determined by GG if the transcendental value of GG is maximum. In particular, we have G/H≤(Z/(2))⊕2, if HH is the alternating group A5A5 and normal in GG.