Determine the center of the dihedral group of order 12.
This was asked in an exam so I presume there must be a more efficient way of doing it than actually going through all the elements of a group G and checking that they commute with every other element.
When searching for an answer online I also came across this question - "The centre of a group $G$ consists of all elements $z$ such that $zg = gz$ for all $g \in G$. For each $n$, find the centre of the dihedral group $D_n$".
Which leads me to believe there must be some formula for determining the centre of a dihedral group of any order.