A rough draft:
I only have membership + message buttons on the card, as don’t think the “delete” button would be used much from the card.
Description may overrun the card in very strange ways, and I didn’t find it very useful to display on the card itself. If you’re looking for a full description of the group, you could navigate to the group page from the card.
Cards look a little dull with no avatars attached to them. What should we do if a group does not have an avatar? My seat of the pants suggestion would be to have fa-users as a placeholder here.
Is showing avatars in the card sufficient to imply membership?