 TOPICS  # Cyclic Group C_5 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. 1    1 1         1    1    1    1   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.

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