Can anyone help me with taking Wreath Products of Groups in Sagemath?
I haven't been able to find a online reference and it doesn't appear to be built in as far as I can tell.
As far as I know, you would have to use GAP to compute them within Sage (and then can manipulate them from within Sage as well). See e.g. this discussion from 2012. This question has information about it, here is the documentation, and here it is within Sage:
F = AbelianGroup(3,[2]*3)
G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
Gp = gap.StandardWreathProduct(gap(F),gap(G))
print Gp
However, if you try to get this back into Sage, you will get a NotImplementedError because Sage doesn't understand what GAP returns in this wacky case (which I hope even is legitimate). Presumably if a recognized group is returned then one could eventually get it back to Sage for further processing. In this case, you might be better off doing some GAP computations and then putting them back in Sage after doing all your group stuff (which isn't always the case).