jerry0 initially inquired about setting a group icon, thinking it was not possible due to the lack of an edit button next to the icon. However, awesomerobot explained that the avatar flair image is used as the group icon on the groups page and group card. jerry0 was pleased to discover this and suggested that the configuration should clarify that the flair image serves this purpose. It was revealed that jerry0 intended to use the group icon as an “avatar” for the group, differing from the typical use as a flair.
By the way, I am not referring to the avatar flair but the icon which appears next to the /groups page and on the group card… such as these on Discourse Meta.
That image on the groups page is actually the avatar flair image — the preview icon on the configuration page is a placeholder for a user’s avatar (to show the flair in context).
It seems that I hope to use the group icon for a different purpose than most people - I am not really using them as flairs but as “avatars” for the groups.
I like your suggestion to clarify that point, but in the meantime thank you very much for the pointers.