[GAP Forum] semidirect product

[Alex Trofimuk]

-- Dear GAP Forum,

Alex Trofimuk asked
My aim is to construct group G of odd order and |G| not divisible by p^5 
for every prime p dividing |G|. Therefore DerivedLength(G)=4.
For example, I found group H:= SmallGroup(1029,11) , 1029=7*7*7*3  and 
DerivedLength(N)=3. Let Aut:= AutomorphismGroup(H). Then I computed 
group B:= SylowSubgroup(Aut,3)  such that |B|=9. Then I constructs 
G:=SemidirectProduct( B, H ), but DerivedLength(G)=3. My question : why 
DerivedLength(G)<>4? Thanks.

Alex Trofimuk.

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