On 08/12/2013 13:38, firstname.lastname@example.org wrote:
> Example: The symmetry group of the utility graph K3,3 has 72 elements > if I googled correctly. So no 3D symmetry group fits. > > If I go to higher symmetry, is *any* group the subgroup > of some R_n (rotation group of dimension n)? Methinks yes, > but already in 4D my head hurts :-)
I am not sure to have understood your question, but if you are asking "Is every finite group isomorphic to a subgroup of the group SO(R,n) of all orientation-preserving linear isometries of R^n, for some _n_?", then yes, it is true. Do you want a proof of this?