Does an effective group action on a compact manifold has $G$ as an orbit?

Question

Recall that a compact manifold $M$ with a $G$-action, where $G$ is a compact Lie group, is such that $M$ contains an open, dense and convex subset where the points have the smaller possible isotropy group.

Assuming the action is effective, does $M$ has a point with trivial isotropy?

Answer 1

This is false.

Consider the $SO(3)$ action on $S^2$. It is effective but every point has isotropy.