How do I create new groups on my iPhone 5, and/or how do I sync to my gmail groups?

I just set up syncing with Gmail Contacts for my wife's iPad this morning. IOS doesn't handle Groups. I've seen lots of gripes about this in many places online. I've also seen it suggested that we should suggest this as a "feature" to Apple. I'm going to look all day today for a place to do this. I hope you will, too. Good luck!