Suppose that $G$ is a compact Lie group with at least two distinct irreducible 3-dimensional representations.

Can one classify those $G$ with the following two properties?
<ol>
<li> For any irreducible 3-dimensional representations $\pi$, the multiplicity of $\pi\otimes\pi$ at the trivial representation is 0. </li>
<li> For any two distinct irreducible 3-dimensional representations $\pi$ and $\pi'$, the multiplicity of $\pi\otimes \pi'$ at the trivial representation is 1. </li>
</ol>