Group isomorphism to graph ismorphism In reading some blogs about computational complexity (for example here)I assimilated the notion that deciding if two groups are isomorphic is easier than testing two graphs for isomorphism. For example, on the stated page it says that graph isomorphism is a more general problem than group isomorphism.

Hence I am posing the following 


  Given a group $G$ can someone give a construction of a graph
  $\Gamma(G)$ of size polynomial in $|G|$ such that $$\Gamma(G) \cong
 \Gamma(H) \iff G \cong H$$ for groups $G$ and $H?$
The reduction is described in a classic paper of Miller.