Do you want to join a Facebook group as a Facebook page? An Article in Facebook Help says that "pages can only request to join groups and can't be invited to join groups".
This isn't strictly true, though. I manage a Facebook group myself and the 'Invite Members' section often suggests pages for me to invite. Some of these are pages I manage, but others are not. For example here you can see that the top two suggestions are clearly pages, neither of which I manage. (I have not included the subsequent suggestions, all individuals, for privacy reasons.)
Whether I manage the invited page or not, the invitation definitely works and the page admin receives a notification.
When I took the above screengrab I was interacting with my group as a page, so it is likely that these suggested pages have previously 'liked' my page. This probably explains why they are popping up in the 'Invite Members' section, along with users who have also 'liked' my page. (In fact, one of the quickest ways to grow a group is to invite the audience of an established page - assuming you have a relevant one of those.)
However I cannot find a way to invite a page that isn't listed in the 'Invite Members' section. So perhaps that is what Facebook Help means when it says that pages "can't be invited to join groups".