[GAP Forum] automorphisms of "large" 2-groups

[Benjamin Sambale]

Thank you for several replies!
Heiko Dietrich pointed out that the computation can be done with Magma 
in a matter of seconds. Also Eamonn O'Brien provided a concrete 
automorphism of order 7.
I like to add that I had no problems with GAP computing automorphism 
groups of very similar groups (of order 2^9).

Best wishes,
Benjamin

Am 10.02.2014 15:55, schrieb Benjamin:
> Dear GAP users,
>
> I need some help with the following task: Consider
>
> P:=SmallGroup(2^9,10477010);
>
> This group satisfies Z(P)=Phi(P)=Omega(P) and Z(P) has order 8. All I 
> want to know is if Aut(P) is a 2-group. The commands 
> AutomorphismGroup(P) and AutomorphismGroupPGroup(P) (using the AutPGrp 
> package) seem to take very long (have been running for hours). 
> Therefore I guess Aut(P) is quite big and definitely not a 2-group. On 
> the other hand, I tried to extend automorphisms of odd order of 
> subgroups and quotient groups without success. In fact, I believe I 
> showed that any nontrivial automorphism of odd order must have order 7 
> (with regular action on Z(P)).
>
> In any case it would be nice to write down a nontrivial automorphism 
> of odd order without knowing them all. Otherwise I would appreciate 
> any argument that Aut(P) is in fact a 2-group.
>
> Many thanks,
> Benjamin
>
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