After reading other comments in this forum, I realized that GMail groups are not synched to the phone (Vibrant in my case). I was able to do a workaround for this problem that may help others who need to group their contacts.
I found that the three contacts that were available for grouping were not Google contacts but had been entered directly into Phone. I exported the Phone contacts (Menu | More | Import/Export) as a vCard file, then imported the vCard file selecting Phone as the target. The contacts were dumped into the Not Assigned group from which I was able to set up all the groups I needed without any problems.
I was going to delete the duplicated Google group but decided to keep it for synching. Since you can export from Google contacts as a vCard file, you can probably copy this file to the SD card and then import directly to the Phone. Until the 2.2 update which hopefully will preserve the Google groups, this serves the purpose for me.
