Fix failed Projection for Perm Wreath Product constructed with hom

Add bugfix test

lib/gprdperm.gi

@@ -861,7 +861,7 @@ local  info, proj, H, degI, degK, constPoints, projFunc;
     proj:=ActionHomomorphism(W,info.components,OnSets,"surjective");
   # Primitive Action, tuple (t_1, ..., t_degI) corresponds
   # to point Sum_{i=1}^degI t_i * degK ^ (i - 1)
-  else
+  elif IsBound(info.productType) and info.productType=true then
     degI := info.degI;
     degK := NrMovedPoints(info.groups[1]);
     # constPoints correspond to [1, 1, ...] and the one-vectors with a 2 in each position,
@@ -895,6 +895,12 @@ local  info, proj, H, degI, degK, constPoints, projFunc;
       return PermList(topImages);
     end;
     proj := GroupHomomorphismByFunction(W, info.groups[2], projFunc);
+  else # weird cases where we use `hom` for the construction of the wreath product
+    H:=info.groups[2];
+    proj:=List(info.basegens,i->One(H));
+    proj:=GroupHomomorphismByImagesNC(W,H,
+      Concatenation(info.basegens,info.hgens),
+      Concatenation(proj,GeneratorsOfGroup(H)));
   fi;
   SetKernelOfMultiplicativeGeneralMapping(proj,info.base);
 

tst/testbugfix/2022-01-05-WreathProduct-With-Hom-Projection.tst

@@ -0,0 +1,16 @@
+# Projection of Perm Wreath Product constructed with optional hom argument #4727
+gap> K := SymmetricGroup(3);;
+gap> H := SymmetricGroup(5);;
+gap> P := SymmetricGroup(7);;
+gap> hom := GroupHomomorphismByImages(H, P, [(1,2), (1,2,3,4,5)], [(2,3), (2,3,4,5,6)]);;
+gap> G := WreathProduct(K, H, hom);;
+gap> g := (4,13,16,10,8)(5,14,17,12,7,6,15,18,11,9)(19,20);;
+gap> g ^ Projection(G);
+(1,4,5,3,2)
+gap> g := (1,3,2)(4,13,9,6,14,7)(5,15,8)(10,18,11,16,12,17);;
+gap> g ^ Projection(G);
+(1,4,2)(3,5)
+gap> g := (1,2,3) ^ Embedding(G, 1) * (1,2) ^ Embedding(G, 4) * (1,2) ^ Embedding(G, 6) * (1,4)(2,3) ^ Embedding(G, 8);
+(1,2,3)(4,13)(5,14)(6,15)(7,10,8,11)(9,12)(16,17)
+gap> g ^ Projection(G);
+(1,4)(2,3)