@ 

The problem is, I think, that it is "only" a DerivedSeries. If you take

the CompositionSeries that is not available in Maple but in GAP then

the points 30 29 21 8 1 are red marked.

Best wishes

Kurt Ewald

@Carl Love 

Thanks but they are normal, look in Maple

IsNormal (sub[8], sub[21]);  true

IsNormal(sub[9],sub[21]);    true

IsNormal(sub[10],sub[21];   true

Kurt Ewald

@Carl Love 

You was very heplful for me in constructing a factory Group.

I am looking for a method to construct the Automorphism Group of a group G as a permutationgroup,

I hope you can help me.

Best regards

Kurt Ewald

@Carl Love 

Hallo,

G:=DihedralGroup(20)

g:=<(1,6,11,16)(2,7,12,17)(3,8,13,18)(4,9,14,19)(5,10,15,20)>

IsSubgroup(g,G)=true

IsNormal(g,G)=true

F:=FactorGroup(G,g)

GroupOrder(F)=40

GroupOrder(G)=40

GroupOrder(g)=10

40/10=4 and not 40.

Why the procedure do fail in this case?

Best regards

Kurt Ewald

@Carl Love Many thanks for the procedure. But some actions, for instance IsNilPotent(GH), fail. But with a little program I can identify the SmallGroup, that is isomorph to GH.

I had found another way, to create the FactorGroup

R:=map(Representative,LeftCosets(H,G)) and then

M:=Group(R).

The results were the same as with your procedure.

But I was not sure, weather my way is allright.

Nevertheless many thanks and best regards

Kurt Ewlad