find the center of the group A4 Solution if G is a group, its center Z(G) is the set of elements that commute with all elements in G, i.e. Z(G)={x in G| xg=gx, for any g in G} A4 stands for the group of even permutations of 4 elements. Since S4 has 4!=24 permutations, A4 will have 12 permutations. So find all these permutations and see if they commute or not , In general the permutations are far of being commutative.