Count and describe the different isomorphism classes of abelian groups of order 1800. I don't need to list the group individually, but I need to give some sort of justification.
The Attempt at a Solution
I'm using the theorem to classify finitely generated abelian groups,
As always we will have Z_1800 to begin with.
Also we know 1800=23(32)(52).
But how do I count all of the possibilities?