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 GroupExplore with Wolfram|Alpha
More things to try:
Cite this as:
Weisstein, Eric W. "Finite Group C_2×C_4." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FiniteGroupC2xC4.html