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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 $\{D\}$.

© 1996-9 Eric W. Weisstein