# Classifying Finite Abelian Groups

## Homework Statement

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?

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