Groups of order 20

Up to isomorphism there are five groups of order \(20\). The abelian ones are \(\ZZ/20\ZZ\) and \((\ZZ/2\ZZ)^2\times\ZZ/5\ZZ\), and the nonabelian ones are

1. the dihedral group \(D_{10}\) of order \(20\),

2. \(\ZZ/5\ZZ\rtimes\ZZ/4\ZZ\) with \(\ZZ/4\ZZ\) acting faithfully, which is the affine group \(\operatorname{AGL}_1(\FF_5)\),

3. the dicyclic group of order \(20\), \[ \gens{a,b\suchthat a^{10}=1,\ b^2=a^5,\ bab^{-1}=a^{-1}}. \]