If you go to your settings page in your group and select a cover photo and a group icon photo, you can customize those and it will apply to both desktop and mobile.Yes, I know I can set the icon. My point is that I have chosen not to set one up for some groups just yet but an icon is shown for those groups on the feed page; On the mobile site for one of my subgroups I see this:
Yet on the feed page, it shows this:
I think the icons shown should be the same on the mobile site and feed page. Personally, I'd prefer standard blue icons I mentioned in my previous post. I don't want random pictures chosen by someone else.