[GAP Forum] wreath product with a sparse permutation group

[Anvita]

Dear Forum,

The manual says that the function

WreathProduct( G, P )

constructs the wreath product of the group G with
the permutation group P (acting on its MovedPoints).
Presumably, this means that the resulting group
should have size

|G|^n * |P|,

where n = Size(MovedPoints(P)).
However, this is not so in the case where P is a
"sparse" permutation group. For example:

--------------------------------------
gap> R:=Group((1,3,5));
Group([ (1,3,5) ])
gap> MovedPoints(R);
[ 1, 3, 5 ]
gap> Size(last);
3
gap> WreathProduct(CyclicGroup(5),R);
<group of size 9375 with 4 generators>
gap> 5^3*3;
375
gap> 5^5*3;
9375
--------------------------------------

Is this the expected behavior?

Thank you,
Anvita