The order statistics of a group $G$ is the multiset of orders of elements of $G$, with multiplicities given by the number of elements in $G$ of that order.

For example, the Quaternion group of order 8 has order statistics $\{1,2,4,4,4,4,4,4\}$ which we denote in searches as 1^1, 2^1, 4^6.