Some airlines will offer a free ticket for every X amount of passengers booked when purchasing group airfare.
For example, on Southwest you receive 1 free ticket for every 29 passengers booked. The airline groups department might quote a 30 passenger group at $600 per passenger, but the total group cost will only charge for 29 passengers.
Total Group Cost:
Without the free ticket: $18,000 (30x600)
With the free ticket: $17,400 (29x600)
Most tour operators simply take the free ticket to reduce the overall cost of the group and apply it as a discount. In the use case above, the operator would quote the group at $580 per passenger($17,400/30). For student and other youth athletic groups, this free ticket is often offered to a coach.
The following airlines offer a free ticket (often referred to as a Tour Conductor ticket):
Note: please note that Tour Conductor tickets are subject to airline policies