Express the commutative group $Z^{3}/(f_{1}.f_{2},f_{3})$ as a direct sum of cyclic group where $f_{1}=(4,6,9), f_{2}=(2,4,12), f_{3}=(4,8,16)$ my answer is $Z[x]/(-11x^{2}+22x-128)$.
I wonder if my calculation is wrong, for this is not a direct sum of cyclic group, hope someone can give me a more clear answer.
How to find the number of non-isomorphic commutative group of a certain order, like $100$ and $p^{3}$ where $p$ is a prime.
I know that I can use Kronecker Decomposition Theorem, finite abelian group theorem.