Sharepoint admin rights

Dear all,

I am currently testing out the new groups feature + all the things that go with it.

One thing however which I am continuously failing at is figuring out is why the admin of the group is also not the admin of the sharepoint website? To make things worse, I am also the global admin and still for some reason whenever I want to change the page settings I am blocked and can send a request to, basically myself. However, even when I grant myself full access i still cannot change the website properties (ex. language).

Naturally, given that groups feature is still kinda in beta i cannot even access the site in sharepoint admin.

Please some help here as, from what I have seen up to now, this feature is amazing and I want to implement it in my company.

Thank you all for all the information you have provided here as it was/is crucial for my understanding of all the great things o365 is offering. 

Cheers!