Finite Group C_2×C_2×C_2

The group C_2×C_2×C_2 is one of the three Abelian groups of order 8 (the other two groups are non-Abelian). An example is the modulo multiplication group M_(24) (which is the only modulo multiplication group isomorphic to C_2×C_2×C_2).


The cycle graph is shown above. The elements A_i of this group satisfy A_i^2=1, where 1 is the identity element.


Its multiplication table is illustrated above.

Each element is in its own conjugacy class. The subgroups are given by {1}, {1,A}, {1,B}, {1,C}, {1,D}, {1,E}, {1,F}, {1,G}, {1,A,B,C}, {1,A,D,E}, {1,A,F,G}, {1,B,D,F}, {1,B,E,G}, {1,C,D,G}, {1,C,E,F}, and {1,A,B,C,D,E,F,G}. Since the group is Abelian, all of these are normal subgroups.

See also

Cyclic Group C8, Dihedral Group D4, Finite Group C2×C4, Quaternion Group

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Cite this as:

Weisstein, Eric W. "Finite Group C_2×C_2×C_2." From MathWorld--A Wolfram Web Resource.

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