 TOPICS  # Cyclic Group C_6 is one of the two groups of group order 6 which, unlike , is Abelian. It is also a cyclic. It is isomorphic to . Examples include the point groups and , the integers modulo 6 under addition ( ), and the modulo multiplication groups , , and (with no others). The cycle graph is shown above and has cycle index The elements of the group satisfy , where 1 is the identity element, three elements satisfy , and two elements satisfy . Its multiplication table is illustrated above and enumerated below. 1     1 1           1     1     1     1     1    Since is Abelian, the conjugacy classes are , , , , , and . There are four subgroups of : , , , and which, because the group is Abelian, are all normal. Since has normal subgroups other than the trivial subgroup and the entire group, it is not a simple group.

Cyclic Group, Cyclic Group C2, Cyclic Group C3, Cyclic Group C4, Cyclic Group C5, Cyclic Group C7, Cyclic Group C8, Cyclic Group C9, Cyclic Group C10, Cyclic Group C11, Cyclic Group C12, Dihedral Group D3

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Weisstein, Eric W. "Cyclic Group C_6." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclicGroupC6.html