Java HotSpot Virtual Machine

Once a day, at around 4-4:30am, our application experiences a single Full GC with taking an exorbitant amount of time. A Full GC kicks in and pauses all threads for 5 to 30 minutes. Full GC's regularly occur at other times and complete in 5-20 seconds. Anyone seen this or any have any ideas about this?

Example of normal GC that occurs frequently throughout the day:

[Full GC[Unloading class $Proxy136]
....
4632722K->1616289K(6141952K), 14.9400110 secs]

Example of ridiculously long GC that occurs daily at 4-4:30am:
[Full GC[Unloading class sun.reflect.GeneratedSerializationConstructorAccessor455]
....
5456231K->2017269K(6141952K), 492.0402160 secs]

Here's our VM params:
-server -XX:-OmitStackTraceInFastThrow -Xincgc -XX:+CMSIncrementalMode -XX:+CMSIncrementalPacing -XX:MaxGCPauseMillis=20000 -XX:+DisableExplicitGC -XX:NewSize=1500m -XX:SurvivorRatio=18 -verbose:gc
-Xms6000M -Xmx6000M

We're running Java 1.6 on Linux, Redhat 3.