This is what I've done so far. For the first part of the problem, we decompose 1350. into a product of primes as . Then we have
Is this right?
And what do I need to do for the second part? How do I identify the ones which are isomorphic to ?
In the last direct product in my list, gcd(3,3,3,2,5,5)=1 i.e. they are relatively prime. Does this mean it is isomorphic to the given group?