Symmetry of Fullerene C60

On analyzing the Euclidean graph of Fullerene C60, we have obtained the automorphism group of the Euclidean graphs of this molecule. It is proven that this group has order 120 and is isomorphic to $Z_2 \times A_5$, where Z2 is a cyclic group of order 2 and A5 is the alternating group on five symbols.