 TOPICS # Cyclic Group C_7 is the cyclic group that is the unique group of group order 7. Examples include the point group and the integers modulo 7 under addition ( ). No modulo multiplication group is isomorphic to . Like all cyclic groups, is Abelian. The cycle graph is shown above, and the group has cycle index is The elements of the group satisfy , where 1 is the identity element. Its multiplication table is illustrated above and enumerated below. 1      1 1             1      1      1      1      1      1     Because it is Abelian, the group conjugacy classes are , , , , , , and . Because 7 is prime, the only subgroups are 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 C5, Cyclic Group C6, 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_7." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclicGroupC7.html