Welcome to Android Central! Open your Google Contacts website on your computer browser, select the contacts group, then click the Menu button at the upper left. Click More, then Export, then choose Outlook CSV. That file should be easily importable into a Hotmail/Outlook.com account.
There's an Export option in the Google Contacts app settings as well, but I think that only exports your entire contact list -- it doesn't look like you can select a specific group to export.