Finite Group C_2×C_4

C_2×C_4 is one of the three Abelian groups of group order 8 (the other two being non-Abelian). Examples include the modulo multiplication groups M_(15), M_(16), M_(20), and M_(30) (and no others).


The elements A_i of this group satisfy A_i^4=1, where 1 is the identity element, and four of the elements satisfy A_i^2=1. The cycle graph is shown above.


Its multiplication table is illustrated above.

Since the group is Abelian, each element is in its own conjugacy class.

The subgroups are {1}, {1,B}, {1,E}, {1,G}, {1,A,B,D}, {1,B,C,F}, {1,B,E,G}, and {1, A, B, C, D, E, F, G}. Since the group is Abelian, all of these are normal.

See also

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

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Cite this as:

Weisstein, Eric W. "Finite Group C_2×C_4." From MathWorld--A Wolfram Web Resource.

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