All I could think of was the direct products of additive integer groups whereas $gcd(m,n) = 1$, such that $m$, $n$ elements of $\mathbb{Z}_{m} \times \mathbb{Z}_{n}$ . A hint would be really helpful.
2026-03-26 08:04:25.1774512265
How many groups are there of order 12?
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This is a very short answer, but I will give two links:
http://www.wolframalpha.com/input/?i=groups+of+order+12
http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/group12.pdf, which proves that the five groups of order $12$ listed in the link in the previous bullet are unique up to an isomorphism, by means of semidirect products.