When we create a group, we should be able to put select an image to be there (like the logo of mathematics or all the pictures the big groups have)
We actually use the logo to designate which groups are "official" and which groups are not right now, so I don't know if we'll do that - but thanks for the suggestion!
Of course, shadowfiend may come back and say otherwise. I, at least, have been given the impression the desire is to keep those separate.
Maybe you could add a frame to the logo. Then you could add a little symbol(like the one that tells which is the level of the user) and a golden frame for the official groups.
It might be useful to also allow us to add a short description of what the group is intended for.
osanseveiro's suggestion is pretty good. You could give a golden border for official groups.
It's been in the back of our minds, but it's not high priority yet. We're cooking up some goodness in a different direction for a little while ;) Rest assured, we know it would be a nice feature and are definitely thinking about it. Same goes for descriptions :)
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