diff --git a/lib/float.gi b/lib/float.gi
index 02f03778c2..2a0588b1a8 100644
--- a/lib/float.gi
+++ b/lib/float.gi
@@ -1058,7 +1058,19 @@ InstallMethod( \^, "for float and rational", ReturnTrue, [ IsFloat, IsRat ], -1,
 end );
 InstallMethod( \^, "for floats", ReturnTrue, [ IsFloat, IsFloat ], -1,
         function ( x, y ) return x ^ MakeFloat(x,y); end );
-        
+
+
+InstallMethod( IsGeneratorsOfMagmaWithInverses,
+    "for a collection of floats (return false)",
+    [ IsFloatCollection ],
+    SUM_FLAGS, # override everything else
+    function( gens )
+    Info( InfoWarning, 1,
+          "no groups of floats allowed because of incompatible ^" );
+    return false;
+    end );
+
+
 #############################################################################
 ##
 #E
diff --git a/tst/testbugfix/2018-03-27-float-group.tst b/tst/testbugfix/2018-03-27-float-group.tst
new file mode 100644
index 0000000000..571186d2d7
--- /dev/null
+++ b/tst/testbugfix/2018-03-27-float-group.tst
@@ -0,0 +1,13 @@
+# Disallow creating groups with non-associative generators.
+# See issue #823
+gap> Group(2.0);
+#I  no groups of floats allowed because of incompatible ^
+Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)
+gap> Group(2.0,3.0);
+#I  no groups of floats allowed because of incompatible ^
+Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)
+gap> Group([], 1.0);
+<trivial group>
+gap> Group([2.0], 1.0);
+#I  no groups of floats allowed because of incompatible ^
+Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)