diff --git a/lib/clashom.gi b/lib/clashom.gi
index 52354e4c8e..537ad2b08b 100644
--- a/lib/clashom.gi
+++ b/lib/clashom.gi
@@ -1130,7 +1130,7 @@ local cs,	# chief series of G
   # we will give classes always by their representatives in G and
   # centralizers by their full preimages in G.
 
-  cs:= ChiefSeriesOfGroup( G );
+  cs:= ChiefSeriesThrough( G,[Socle(G)] );
 
   # the first step is always simple
   if HasAbelianFactorGroup(G,cs[2]) then
@@ -1719,8 +1719,6 @@ BindGlobal("LiftClassesEANonsolvGeneral",
   
   # Construct matrices for the affine operation on $N/[h,N]$.
   Info(InfoHomClass,4,"space=",Size(field),"^",r);
-  if Size(field)^r>3*10^8 then Error("too large");fi;
-  aff := ExtendedVectors( field ^ r );
 
   gens:=Concatenation(cl[2],Npcgs,cl[3]); # all generators
   gpsz:=cl[5];
@@ -1745,7 +1743,9 @@ BindGlobal("LiftClassesEANonsolvGeneral",
     Add( imgs, M );
   od;
 
-#if Size(field)^r>10^7 then Error("BIG");fi;
+
+  if Size(field)^r>3*10^8 then Error("too large");fi;
+  aff := ExtendedVectors( field ^ r );
 
   # now compute orbits, being careful to get stabilizers in steps
   #orbreps:=[];
diff --git a/tst/testbugfix/2022-04-19-conjcl.tst b/tst/testbugfix/2022-04-19-conjcl.tst
new file mode 100644
index 0000000000..004e7832a0
--- /dev/null
+++ b/tst/testbugfix/2022-04-19-conjcl.tst
@@ -0,0 +1,7 @@
+# ConjugacyClasses, #4866
+gap> g:=Group((9,11)(12,14)(15,17)(18,20)(21,23)(24,26)(27,29)(30,32)(33,35)
+> (36,38),(9,39)(11,40)(13,42)(15,44)(17,45)(19,46)(21,47)(23,49)(25,51)
+> (27,52)(29,53)(31,54)(33,56)(35,58)(37,59), (7,8)(10,11)(15,16)(20,21)
+> (25,26)(30,31)(35,36)(40,41)(43,44)(47,48)(50,51)(54,55)(57,58));;
+gap> Length(ConjugacyClasses(g));
+1308