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## 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.

## Homework Equations

## 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=2

^{3}(3

^{2})(5

^{2}).

But how do I count all of the possibilities?

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