Git user account and public ssh key


I have a self-hosted GitLab Omnibus installation. I am trying to mirror a specific branch of one of my projects to a GitHub public repo (branch is named release)

The idea is to use project specific post-receive hook. I have created a post receive hook to push said branch to a remote named github. I have defined the remote in config file.

The problem is that in order for this to work I have to enable deployment with write access in GitHub and do that I need a public rsa key. I know GitLab is using git user on the system to do all git related operations but I don’t know how to create/retrieve the ssh key for the git user.

Any help would be appreciated.