I agree that this is something the President should address. If the people that volunteered to help run the group aren't doing the things necessary to continue to run the group, then one of two things needs to happen:
1. The group disbands.
2. People that are passionate about continuing the group, step up and fill the void.
People can't have it both ways. They can't say that they want to continue having the group but don't want to do anything to keep it going. Like others have said, if you continue to volunteer to fill the gap, then there's no reason for anyone else to do it. So, be very clear about what you can and cannot contribute to the President and then only do that. If that means that the group falls apart and you have to find someplace else to go, then so be it.
As for the socializing part, I get how hurtful and frustrating that is. I don't necessarily think, though, that just because the group allows you to do most of the work, that they have to socialize with you outside of the group...but, I do think they are being insensitive and your feelings are quite understandable. This, again, points to the fact that if you always do the work, then there's no reason for anyone else to do it. So, speak to the President and then only do what you volunteered to do and let the cards fall from there.