Latin square and groups From what I can gather, table of each group present latin square. But I wonder, how can I give an example of latin square which isn't a result of the operations on group?

\begin{array} & &2 &1 &3 \\\ &1 &3 &2 \\\ &3 &2 &1 \\\ \end{array}

This cannot represent a group because there is no identity element. $1*1=2$, $2*2=3$, and $3*3=1$.