Give an example of a non-cyclic group of order 49. I have a couple problems like this. I think there are only two isomorphism class for order 49, Z_49 and Z_7 x Z_7. since Z_49 is cyclic, I'm guessing Z_7 x Z_7 is non-cyclic. Right? A related question is "is there a non-cyclic group of order 39? there are two classes of isomorphism here, Z_39 which is cyclic, and Z_13 x Z_3 which I don't know if is cyclic. how can I tell?