Clearification about order of groups

[spacenerd]

When a group has a prime order, does that mean that it is always isomorphic to the cyclic group of the same order? I just am a little confused and need some clarification on this matter.
Thanks

 

[micromass]

Yes! If a group has a prime order p, then the group has to be isomorphic to \mathbb{Z}_p!

 

[spacenerd]

Thanks :)

 

[Robert1986]

Thanks :)

I see that you have had your question answered, but can you think of an isomorphism between any two groups of order p where p is prime? I think if you do this, you might understand it even more.