Because the group is active, the group currently has page and trust authority with Google. And it's probably passing a lot of juice to your website, especially if people in the group are talking about your business.
If you convert the group to a page and the URL changes, you might lose all of that page and trust authority. Because this would essentially be deleting a good page from the web. If the group posts by users talking about your site are deleted in the process, all of those brand mentions and website links are also removed.
If you can retain the group posts and the URL, you can retain the page authority. But if not, it's potentially a lot to lose.
By setting up a page about the site instead of a group, you have an opportunity to curate content on the page which could make the page's content stronger. Thus, the page could end up having stronger trust with Google in the future. But if people are unable to post to the page, all of those potential brand mentions and links could be a missed opportunity.
If there's a way to turn it into a page without losing all of the current benefits of the group, then by all means try to go for it. But because I think it's possible you might lose a lot, you might want to try and expand into a page while keeping the group. Sometimes you have to go with what works. Moving a working vehicle into something even stronger is a good thing, but deleting a working vehicle to replace it with something else is another. I'm not sure which one this is exactly.