Facebook API - POST a comment on a private groups post

Question

I have successfully retrieved an post made on an private group and the comments made on this post. I want also to make the users on my app to be able to reply to comments on that post but cant get my head around this problem. This is the API URL to GET all the comments on an post ID.

1338804626636796_1351943298656262/comments

When i try to do a POST call to this URL i get as a result:

{   "error": {
     "message": "(#3) Publishing comments through the API is only available for page access tokens",
     "type": "OAuthException",     
      "code": 3,     
      "fbtrace_id": "AM6a-he8gLoFA8SDVHjfDYO"   
    } 
}

As far as i understand Page Access Token is used to manage Pages... Im working with Groups not Pages, and when i try to create a Page Access Token my Group that i want to manage wont show up ofcourse.

I then follow this guide: Get a page Access Token API Docs

It asks for a PAGE ID, i have group ID but i try it anyways and get this as a response:

code: 100 fbtrace_id: "AnzTkEAsbp8s-Z__QawDBYX" message: "(#100) Tried accessing nonexisting field (access_token) on node type (Group)" type: "OAuthException"