Restricted Burnside group:RB(2,5)

Definition
This group is defined as the restricted Burnside group with parameters 2,5. In other words, it is the quotient by the finite residual of the Burnside group $$B(2,5)$$, which in turn is defined as the quotient of the free group of rank two by the intersection of all its normal subgroups of finite index.

The group turns out to be a finite group (this is a special case of Kostrikin's theorem on restricted Burnside problem). Thus, it can also be defined as the largest size finite group that is a 2-generator group and has exponent five.