is the unique group
of group order 5, which is Abelian .
Examples include the point group and the integers mod 5 under addition ( ). No modulo multiplication
group is isomorphic to .

The cycle graph is shown above, and the cycle
index

The elements
satisfy ,
where 1 is the identity element .

Its multiplication table is illustrated above
and enumerated below.

Since
is Abelian, the conjugacy classes are , , , , and . Since 5 is prime, there are no subgroups except the trivial
group and the entire group. is therefore a simple group ,
as are all cyclic graphs of prime order.

See also Cyclic Group ,

Cyclic Group C2 ,

Cyclic Group C3 ,

Cyclic
Group C4 ,

Cyclic Group C6 ,

Cyclic
Group C7 ,

Cyclic Group C8 ,

Cyclic
Group C9 ,

Cyclic Group C10 ,

Cyclic
Group C11 ,

Cyclic Group C12
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Cite this as:
Weisstein, Eric W. "Cyclic Group C_5."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/CyclicGroupC5.html

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