[GAP Forum] automorphisms of "large" 2-groups
Benjamin
benjamin.sambale at gmail.com
Mon Feb 10 14:55:44 GMT 2014
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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