Finite Group Z5

The unique Group of Order 5, which is Abelian. Examples include the Point Group $C_5$ and the integers mod 5 under addition. The elements $A_i$ satisfy ${A_i}^5=1$, where 1 is the Identity Element. The Cycle Graph is shown above, and the Multiplication Table is illustrated below.

$Z_5$	1	$A$	$B$	$C$	$D$
1	1	$A$	$B$	$C$	$D$
$A$	$A$	$B$	$C$	$D$	1
$B$	$B$	$C$	$D$	1	$A$
$C$	$C$	$D$	1	$A$	$B$
$D$	$D$	1	$A$	$B$	$C$

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