It's well-known that on a Riemannian manifold $(M,g)$ with dimension larger than 2, the dimension of its conformal group $\text{conf}(M,g)$ is bounded above by ${n+2\choose 2}$. A Riemannian manifold whose conformal group has the maximum possible dimension is said to have a "large" conformal group. Some important examples include semisimple Lie groups that act by fractional linear transformations on manifolds, such as $SO(n+1,1)$, the conformal group of the standard $n$-sphere, and $SO(4,2)$, the conformal group of Minkowski space.


Now let's call any Lie group of transformations on $(M,g)$ "small" if that group is a discrete group.


There are plenty of examples of Riemannian manifolds with small *isometry* groups. In fact there's a neat paper ([Asimov, 1976](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAA&url=http%3A%2F%2Fwww.ams.org%2Ftran%2F1976-216-00%2FS0002-9947-1976-0390959-4%2FS0002-9947-1976-0390959-4.pdf&ei=aL0QVPSRH4PTiwKty4GIAw&usg=AFQjCNGGsLi63kvMvKcJAZQdYRE0UIN8Ig&sig2=Fqp7M2-kVF8tiUWn2VqtTQ&bvm=bv.74894050,d.cGE)) which shows that if $G\_{k+1}$ is a finite group with $k+1$ elements, then there exists a Riemannian metric on the $(k-1)$-sphere such that its isometry group is isomorphic to $G\_{k+1}$.


**Question:** Are there examples of Riemannian manifolds with small conformal groups?



Large and Small Conformal Groups
By the so-called conformal Lichnerowicz conjecture (proved by Alekseevsky, Ferrand, Schoen) a manifold has either big conformal group or there exists a metric in the conformal class such that the conformal group acts by isometries of this metric. Thus, the answer to your question is the same as for the isometry group 


