# Minimal block system in GAP software

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 $G=\langle (12)(34),(13)(24),(14)(23) \rangle$ $$\pi: G \times [4] \mapsto [4]$$

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.

Try RepresentativesMinimalBlocks(G,MovedPoints(G)). It will give for each block system the block containing $1$. If $r$ is such a block Orbit(g,Set(r),OnSets) will return the full block system.

• Thanks for the answer but, RepresentativesMinimalBlocks(G,MovedPoints(G)) is not working. it is not giving the minimal block system. – user437890 Oct 29 '17 at 4:54
• @sssss Can you give me a concrete example of what is not working (group generators and the error message you get)? -- possibly just by personal mail. – ahulpke Oct 29 '17 at 16:46
• @ ahulpke Sorry . It is working correctly, it was my mistake. – user437890 Oct 30 '17 at 7:58