Sep 7, 2016 - 10:35 AM
Welcome to MySwissAlps! You will need to reserve for such a large group, but I don't know how far in advance this should be done. The same day seems rather late to me. I would reserve the day before, during office hours, after checking the weather forecast. Best time of the day depends on the forecast as well. In general mornings are better.
Groups get a 20% discount on tickets, but it would be worth it to check whether rail passes are worth it for your group. Whether it is depends on your other travel plans. Swiss Half Fare Cards might be worth it. It will get you a 50% discount on this trip, and many others too: myswissalps.com/ swisshalffarecard.