Which group of order must be abelian?

Could you please elaborate on which group of order necessarily exhibits the abelian property? It's intriguing to understand the mathematical conditions under which a group becomes commutative, meaning the order of multiplication does not affect the result. Are there specific criteria, such as the number of elements or certain algebraic structures, that guarantee a group will be abelian? I'm particularly interested in learning about the necessary conditions that make a group abide by the commutative law.