Redirected from Trivial group
The notation G × H stands for the direct product of the two groups.
Order | Groups |
---|---|
1 | C1 (the trivial group, abelian) |
2 | C2 (abelian, simple) |
3 | C3 (abelian, simple) |
4 | C4 (abelian); C2 × C2 (abelian, isomorphic to the Klein four-group). |
5 | C5 (abelian, simple) |
6 | C6 (abelian); S3 (isomorphic to D6, the smallest non-abelian group) |
7 | C7 (abelian, simple) |
8 | C8 (abelian); C2 × C4 (abelian); C2 × C2 × C2 (abelian); D8; Q8 (the quaternion group) |
9 | C9 (abelian); C3 × C3 (abelian) |
10 | C10 (abelian); D10 |
11 | C11 (abelian, simple) |
12 | C12 (abelian); C2 × C6 (abelian); D12; A4; the semidirect product of C3 and C4, where C4 acts on C3 by inversion. |
13 | C13 (abelian, simple) |
14 | C14 (abelian); D14 |
15 | C15 (abelian) |
It contains explicit descriptions of the available groups in computer readable format.The library has been constructed and prepared by Hans Ulrich Besche, Bettina Eick and Eamonn O'Brien; see http://www.tu-bs.de/~hubesche/small .
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