Weak 2-groups can be classified by the data $(\pi_1,\pi_2, t, \omega)$, where $\pi_1$ is a group, $\pi_2$ an Abelian group, $t: \pi_1 \to Aut(\pi_2)$, and $\omega \in H^3(B\pi_1,\pi_2)$.

I wonder do we have a similar classification for weak three groups?

3-groups contain data $(\pi_1,\pi_2,\pi_3)$ (three groups). I am interested in the simple cases where $\pi_2$ is $Z_2$ or trivial and $\pi_3$ is $U(1)$ or $Z_n$.