Non-power-associative loop of order five

Definition
This is a loop with five elements. Up to isomorphism, it is the only loop of five elements that is not a power-associative loop.

In other words, this is the algebra loop corresponding to the Latin square:

$$\begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 1 & 5 & 3 & 4 \\ 3 & 5 & 4 & 2 & 1 \\ 4 & 3 & 1 & 5 & 2 \\ 5 & 4 & 2 & 1 & 3 \\\end{pmatrix}$$