Loop of order five and exponent two

Definition
This loop is defined by the multiplication table:

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

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