How to group consecutive rows having same event and find average?

Value <- c(2,3,5,2,5,8,17,3,5)
Event <- c(1,1,2,2,2,1,1,2,2)

group <- data.frame(pt=Value, Event=Event)

I have data like above and I would like to group events in a way that would result into following.

Event Value
1     2.5
2     4
1     12.5
2     4

Thank you in advance.