I have created a default custom property for groups, I made it visible to group admins.
When  I edited a group there was no sign of the custom field.
I changed it so it was visible to Site Admins, still not displayed.

Any ideas?

Also I don't seem to be able to edit the custom property.

Tried in IE8 and FF3.6.6
DNN 4.9.5, AS 1.7.1

Are you using a custom theme?

I am using the '_ActiveSocial' theme.

When I edit the group I do see a section header 'Other Information' ath the bottom but there are no fields displayed.

I just added another group property and left it as visible to everyone and required.

It now shows.

I am logged in as an Admin user.

Just managed to edit the original property and set the visibility to 'everyone', it now displays.

Does it display for you on the group info tab?

Yes both display on info tab.

Sorry looks like a wild goose chase, the group I was testing with was created by 'Superuser'!
It was probably the first group I ever created and did it straight away after installing AS.
I have now changed group owner and all is behaving as it should.

I hang my head in shame, let this be a warning to others.

(laughing)...I think we have all had to 'hang our heads in shame' a few times.  Now go to your room!