Proof:

The Klein four-group (tableau: )$\displaystyle \begin{pmatrix}\circ & e & a & b & c\\ \hline e&e&a&b&c\\ a&a&e&c&b\\ b&b&c&e&a\\ c&c&b&a&e \end{pmatrix} $ is not a cyclic group

First I thought it is not cyclic because the Klein four-group is not commutative, but according to the tableau my guess is wrong.

Any help is much appreciated.

Rapha