The cyclic group is unique group of group order 11. An example is the integers modulo 11 under addition (). No modulo multiplication group is isomorphic to . Like all cyclic groups, is Abelian.

The cycle graph of is shown above. The cycle index is

Its multiplication table is illustrated above.

Because the group is Abelian, each element is in its own conjugacy class. Because it is of prime order, the only subgroups are the trivial group and entire group. is therefore a simple group, as are all cyclic graphs of prime order.