Sorry about not posting links. You are correct about the Genesis Group. You can find some basic info about them at http://www.ldsgenesisgroup.org/ . Awhile ago I encountered an interview of their president, Darius Gray, describing some of their activities..

People might think that the Genesis group just meets in one group all by itself. But in fact, my understanding is you meet in the wards of where ever you are, but once a month you come together. Let’s clear up the misconception about how you meet, when you meet, etc.

We meet once a month. We are all active in our own wards, and we hold positions, many of us, in our own home wards in our stakes. Then we come together and share and celebrate who we are. We don’t have to lose our culture. We don’t have to lose our racial identity to be within the gospel.

We come together. It’s kind of like an LDS meeting that you might find in a sacrament meeting, but you don’t hear an “Amen” in an LDS sacrament meeting. But you can hear that at Genesis. There isn’t a pause after a musical number in a LDS sacrament meeting, and there generally is in Genesis. You generally don’t hear gospel or spirituals in an LDS meeting, and we do at Genesis. So, we’re a blend — we have LDS, we have our racial backgrounds, our cultural backgrounds, and they go together very well. You don’t have to have one exclusion of the other.

http://www.kued.org/productions/voices/interviews/gray.htm