A player in my game will play a fighter with a greatsword. At 5th level he has Extra Attack and the option to use Action Surge. PHB p.72 states:
Action Surge. Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On your turn, you can take one additional action on top of your regular action and a possible bonus action.
Once you use this feature, you must finish a short or long rest before you can use it again. Starting at 17th level, you can use it twice before a rest, but only once on the same turn.
Extra Attack. Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
The number of attacks increases to three when you reach 11th level in this class and to four when you reach 20th level in this class.
The questions and answers that I find on here deal with multi-classing or Two Weapon fighting specifically, which don't really give a clear yes or no on my question.
The way I read these two features is that when a fighter takes an Attack action, he gets the Extra Attack. After using Action Surge he gets the opportunity to take another Attack action, and with that another Extra Attack. This results in four attacks with the greatsword in one turn, which sounds amazing but also rather powerful. Is this correct, or am I missing something?