diff --git a/lib/morpheus.gi b/lib/morpheus.gi
index 3569b1b529..4c81c4c2d0 100644
--- a/lib/morpheus.gi
+++ b/lib/morpheus.gi
@@ -2491,7 +2491,9 @@ local A;
     #LoadPackage("autpgrp"); # try to load the package if it exists
     A:=AutomorphismGroupNilpotentGroup(G);
   elif IsSolvableGroup(G) then
-    if HasIsFrattiniFree(G) and IsFrattiniFree(G) then
+    # AutomorphismGroupFrattFreeGroup needs a pcgs for subgroups of G, which
+    # is not available for example for finitely presented groups
+    if CanEasilyComputePcgs(G) and IsFrattiniFree(G) then
       A:=AutomorphismGroupFrattFreeGroup(G);
     else
       # currently autactbase does not work well, as the representation might
diff --git a/tst/testinstall/opers/AutomorphismGroup.tst b/tst/testinstall/opers/AutomorphismGroup.tst
index 6bce34f984..c45f635051 100644
--- a/tst/testinstall/opers/AutomorphismGroup.tst
+++ b/tst/testinstall/opers/AutomorphismGroup.tst
@@ -24,8 +24,22 @@ true
 # solvable group
 gap> G:=DihedralGroup(100);
 <pc group of size 100 with 4 generators>
+gap> IsFrattiniFree(G);
+false
 gap> AutomorphismGroup(G);
 <group of size 1000 with 4 generators>
 
+# solvable Frattini-free groups, handled by AutomorphismGroupFrattFreeGroup
+gap> G:=SymmetricGroup(4);;
+gap> IsFrattiniFree(G);
+true
+gap> Size(AutomorphismGroup(G));
+24
+gap> Size(AutomorphismGroup(SymmetricGroup(IsPcGroup,4)));
+24
+gap> G:=Group((1,2,3,4,5),(2,3,5,4));;  # Frobenius group of order 20
+gap> Size(AutomorphismGroup(G));
+20
+
 #
 gap> STOP_TEST("AutomorphismGroup.tst");