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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 $\{F\}$.

© 1996-9 Eric W. Weisstein