[GAP Forum] Question about SubdirectProduct

[German Combariza]

Dear all,

I am having problems with the function SubdirectProduct. Looks like GAP does not recognize the SubdirectProduct as a subgroup of the DirectProduct, but It does for small groups.

Example:

s4  := Group((1,2,3,4),(1,2));;
list := AllSmallGroups(48);;
n := 48;;
g := list[n];;
hom := AllHomomorphisms(list[n], s4)[53];;
gamma := SubdirectProduct(g,g,hom,hom);;
wprod := DirectProduct(g,g);;
IsSubgroup( wprod, gamma);  # This is False

However:
g := Group((1,2,3),(1,2));;
k  := Group((1,2));;
hom := AllHomomorphisms(g, k)[2];;
gamma := SubdirectProduct(g,g,hom,hom);;
wprod := DirectProduct(g,g);;
IsSubgroup( wprod, gamma);  # This is true.

Thanks!