I want to list down all minimal block system, I am trying "Blocks(G,[1..4]);" command but it is not giving minimal block system. Let $G=\langle (12)(34),(13)(24),(14)(23) \rangle$ $$\pi: G \times  \mapsto $$
Minimal block system : First consider the group action ($\phi$) of $G$ on $[n]$, then we will be get the blocks , so we need to refine $G$ means at the second level from the leafs, we will consider the action of group $G/Ker(\phi)$ and so on.
Is there any inbuilt command to print all minimal block systems? Thank you.