We present a method, based on an old idea of Serre, for completely computing Frobenius classes in alternating groups. We contrast this method with other approaches in examples involving the alternating groups A3 and A9. The method can be useful for proper subgroups of alternating groups as well, and we present examples involving the 168-element group PSL2(7) = GL3(2) and the Mathieu group M24.
