Finite Group Z6

One of the two groups of Order 6 which, unlike $D_3$, is Abelian. It is also a Cyclic. It is isomorphic to $Z_2\otimes Z_3$. Examples include the Point Groups $C_6$ and $S_6$, the integers modulo 6 under addition, and the Modulo Multiplication Groups $M_7$, $M_9$, and $M_{14}$. The elements $A_i$ of the group satisfy ${A_i}^6=1$, where 1 is the Identity Element, three elements satisfy ${A_i}^3=1$, and two elements satisfy ${A_i}^2=1$. The Cycle Graph is shown above, and the Multiplication Table is given below.

$Z_6$	1	$A$	$B$	$C$	$D$	$E$
1	1	$A$	$B$	$C$	$D$	$E$
$A$	$A$	1	$E$	$D$	$B$	$C$
$B$	$B$	$E$	1	$A$	$C$	$D$
$C$	$C$	$D$	$A$	1	$E$	$B$
$D$	$D$	$B$	$C$	$E$	1	$A$
$E$	$E$	$C$	$D$	$B$	$A$	1

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

See also Finite Group D3