When is Gene's birthday from A Separate Peace?

Gene's birthday is at the end of the summer. We can infer from the text that he likely has an August birthday.

What if they lower the draft age to seventeen? Gene and I are both going to be seventeen at the end of the summer, which is a very convenient time since it’s the start of the academic year and there’s never any doubt about which class you should be in. Leper Lepellier is already seventeen, and if I’m not mistaken he will be draftable before the end of this next academic year, and so conceivably he ought to have been in the class ahead, he ought to have been a senior now, if you see what I mean, so that he would have been graduated and been all set to be drafted.