[GAP Forum] Order and Size

[Benjamin Sambale]

Dear GAP users,

I'm using GAP 4.7.2 and just ran into the following strange behavior:

G:=AbelianGroup([4,4,4]);;
A:=AutomorphismGroup(G);;
x:=First(A,a->Order(a)<>Size(Group(a)));
[ f1*f2*f3, f5, f1*f2*f6 ] -> [ f1, f1*f2*f4*f5*f6, f2*f3*f6 ]

I thought that the order of an element is the same as the size of the 
generated group?? Indeed:

x^Order(x);
Pcgs([ f1, f2, f3, f4, f5, f6 ]) -> [ f1, f2, f3, f4, f4*f5*f6, f6 ]

Any ideas?

Best wishes,
Benjamin