Multiplicative Group of Reduced Residues Modulo 7/Cayley Table

Cayley Table for Multiplicative Group of Reduced Residues Modulo 7
The multiplicative group of reduced residues modulo $7$:
 * $\Z'_7 = \set {\eqclass 1 7, \eqclass 2 7, \eqclass 3 7, \eqclass 4 7}, \eqclass 5 7, \eqclass 6 7$

can be described completely by showing its Cayley table:
 * $\begin{array}{r|rrrr}

\times_5 & \eqclass 1 7 & \eqclass 2 7 & \eqclass 3 7 & \eqclass 4 7 & \eqclass 5 7 & \eqclass 6 7 \\ \hline \eqclass 1 7 & \eqclass 1 7 & \eqclass 2 7 & \eqclass 3 7 & \eqclass 4 7 & \eqclass 5 7 & \eqclass 6 7 \\ \eqclass 2 7 & \eqclass 2 7 & \eqclass 4 7 & \eqclass 6 7 & \eqclass 1 7 & \eqclass 3 7 & \eqclass 5 7 \\ \eqclass 3 7 & \eqclass 3 7 & \eqclass 6 7 & \eqclass 2 7 & \eqclass 5 7 & \eqclass 1 7 & \eqclass 4 7 \\ \eqclass 4 7 & \eqclass 4 7 & \eqclass 1 7 & \eqclass 5 7 & \eqclass 2 7 & \eqclass 6 7 & \eqclass 3 7 \\ \eqclass 5 7 & \eqclass 5 7 & \eqclass 3 7 & \eqclass 1 7 & \eqclass 6 7 & \eqclass 4 7 & \eqclass 2 7 \\ \eqclass 6 7 & \eqclass 6 7 & \eqclass 5 7 & \eqclass 4 7 & \eqclass 3 7 & \eqclass 2 7 & \eqclass 1 7 \\ \end{array}$