The notation G × H stands for the direct product of the two groups.
Order  Groups 

1  C_{1} (the trivial group, abelian) 
2  C_{2} (abelian, simple) 
3  C_{3} (abelian, simple) 
4  C_{4} (abelian); C_{2} × C_{2} (abelian, isomorphic to the Klein fourgroup). 
5  C_{5} (abelian, simple) 
6  C_{6} (abelian); S_{3} (isomorphic to D_{6}, the smallest nonabelian group) 
7  C_{7} (abelian, simple) 
8  C_{8} (abelian); C_{2} × C_{4} (abelian); C_{2} × C_{2} × C_{2} (abelian); D_{8}; Q_{8} (the quaternion group) 
9  C_{9} (abelian); C_{3} × C_{3} (abelian) 
10  C_{10} (abelian); D_{10} 
11  C_{11} (abelian, simple) 
12  C_{12} (abelian); C_{2} × C_{6} (abelian); D_{12}; A_{4}; the semidirect product of C_{3} and C_{4}, where C_{4} acts on C_{3} by inversion. 
13  C_{13} (abelian, simple) 
14  C_{14} (abelian); D_{14} 
15  C_{15} (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.tubs.de/~hubesche/small .
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