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.

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.