Finite Group Z7

The unique Group of Order 7. It is Abelian and Cyclic. Examples include the Point Group $C_7$ and the integers modulo 7 under addition. The elements $A_i$ of the group satisfy ${A_i}^7=1$, where 1 is the Identity Element. The Cycle Graph is shown above.

$Z_7$	1	$A$	$B$	$C$	$D$	$E$	$F$
1	1	$A$	$B$	$C$	$D$	$E$	$F$
$A$	$A$	$B$	$C$	$D$	$E$	$F$	1
$B$	$B$	$C$	$D$	$E$	$F$	1	$A$
$C$	$C$	$D$	$E$	$F$	1	$A$	$B$
$D$	$D$	$E$	$F$	1	$A$	$B$	$C$
$E$	$E$	$F$	1	$A$	$B$	$C$	$D$
$F$	$F$	1	$A$	$B$	$C$	$D$	$E$

The Conjugacy Classes are $\{1\}$, $\{A\}$, $\{B\}$, $\{C\}$, $\{D\}$, $\{E\}$, and $\{F\}$.