diff --git a/gap/structure.gi b/gap/structure.gi
index 0d1e5c0..4f3b8d7 100644
--- a/gap/structure.gi
+++ b/gap/structure.gi
@@ -33,13 +33,17 @@ end);
 
 InstallGlobalFunction(CloneOfTypeByGenerators,
   function(cat, fam, gens, genAttrib, tableCstr)
-    local M;
+    local M, elf;
     if not(IsEmpty(gens) or IsIdenticalObj(FamilyObj(gens), fam)) then
       Error("<fam> and family of <gens> do not match");
     fi;
     M := Objectify(NewType( fam, cat and IsAttributeStoringRep), rec());
     Setter(genAttrib)(M, AsList(gens));
     SetConstructorFromTable(M, tableCstr);
+    elf := ElementsFamily(fam);
+    # Since there doesn't seem to be a way to make the IsFinite method based
+    # on the family being finite into an immediate method:
+    if HasIsFinite(elf) and IsFinite(elf) then SetIsFinite(M, true); fi;
     return M;
 end);