[GAP Forum] elements of wreath products?

[R. Keith Dennis]

I'm sure this is trivial, but the reference manual seems unclear on
this, and the "obvious" thing doesn't seem to work.  If one looks at a
wreath product W:=WreathProduct(G,P), and thinks of an element as
being represented as a product bp (or the other way around) where b is
in the base group and p is in the permuation group P (b =
(b_1,...,b_n), the simplest version:  G^n semi P, where n is the order
of P), how does one find the coordinates of an element w in W?  I.e.,
the b_i.  Presumably this should be given by Image(Projection(W,i),w)
for i between 1 and n, however that leads to an error message.  It
seems I'm missing something.  What?

Thanks.

Keith