Where is the team Galactic special key?

To find the Galactic HQ special key, you first need to fight Team Galactic at the three lakes. The last one being Lake Acruity which is blocked by some Grunts until you aquire the icile badge. Once this is done and you return to the HQ, there will be a grunt outside looking at a satellite dish talking to himself, approach him and he will run away dropping a galactic key :)