which describes various kinds of group extensions.
C4×C2 has C22 as a normal subgroup. The quotient group is C2. Therefore C4×C2 is an extension of C22 by C2. This page shows how.
Call the elements of the normal subgroup N {1,p,q,r}. Call the elements of the quotient group H {1,x}. The extension is defined by a map from H×H to N. This map is specified by colouring the Cayley table of H like this:
| * | 1 | x |
|---|---|---|
| 1 | 1 | x |
| x | x | 1 |
The pink cell of this table generates the element p, which goes into the normal subgroup.
The resulting group is the direct product of {1,x,p,px} and {1,q}.
This is a sub-page of Groups of order 8, regarded as Extensions
which describes various kinds of group extensions.
See also my main index page for groups.
Copyright N.S.Wedd 2008