Construction of $SL(2,5)^4$ in a maximal subgroup in Magma

Question

There is a Class $2$ maximal subgroup $SL(2,5)^{4}.4^{3}.S_{4}$ (denoted by $MM_2$ in the following code) in $PGL(8,5)$. I am trying to locate the $SL(2,5)^4$ part in Magma. But after I constructed some derived subgroups, it seems I've gone a bit further than I'm supposed to.

   K:=GF(5);
   G:=GL(8,K);
   V:=VectorSpace(G);
   phi,G1:=OrbitAction(G,sub<V|V.1>);

   d1:=ClassicalMaximals("L",8,5:general:=true,classes:={2});
    MM2:=phi(d1[2]);

    DER:=DerivedSubgroup(MM2);
    DER:=DerivedSubgroup(DER);
    DER:=DerivedSubgroup(DER);
    #DER;
    829440000
    DER:=DerivedSubgroup(DER);
    #DER;
    103680000
    #SL(2,5)^4;
    207360000

Is the derived-subgroup approach not suitable or something off with $MM_2$? Thank you.