Finite Group Z2

The unique group of Order 2. $Z_2$ is both Abelian and Cyclic. Examples include the Point Groups $C_s$, $C_i$, and $C_2$, the integers modulo 2 under addition, and the Modulo Multiplication Groups $M_3$, $M_4$, and $M_6$. The elements $A_i$ satisfy ${A_i}^2=1$, where 1 is the Identity Element. The Cycle Graph is shown above, and the Multiplication Table is given below.

$Z_2$	1	$A$
1	1	$A$
$A$	$A$	1

The Conjugacy Classes are $\{1\}$ and $\{A\}$. The irreducible representation for the $C_2$ group is $\{1,-1\}$.