Application of class equation

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The class equation is defined on finite group $G$ with $a\in G$, then

$|G|=\sum_{s}|G:C(a)|$ where $s$: sum runs over elements from distinct conjugacy classes. My question what are the applications of this class equation ??

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One of the application is to prove the following result:

The center of any finite $p$-group is non-trivial.