We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$mid$x$mid$$sigma$$mid$u$mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1<p<(n+2)/(n-2), $sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.