Group Theory - specific non-abelian case

[audiowize]

1. The problem statement, all variables and given/known data

Let G be an Abelian group and let H+{x^3 : x is an element of G}

Find a non-Abelian group in which H is not a subgroup

2. Relevant equations

I wish it was that easy...

3. The attempt at a solution

I looked at the quaternion group, and some other matrix groups, but no luck so far...

[matt grime]

What is the first non-abelian group in any reasonable ordering?

[audiowize]

The permutation group S_3.

I looked at this also... but the cubes of the individual elements seemed closed under the operation of composition, and the identity is present... Four of us have spent about 3 hours on this without much luck, any nudging is greatly appreciated!

[Billy Bob]

You should triple-check your work, because matt is never wrong. If G=S_3, what are you thinking H is?

[audiowize]

Thanks for the help guys! I'm sure glad I don't have to take exams at midnight. A fresh set of eyes in the morning and your confirmation sure helped!