The gluteal muscles
The gluteus maximus is the largest of the gluteal muscles and one of the strongest muscles in the human body. It inserts at the iliotibial band and the gluteal tuberosity of the femur. Its action is to extend and to laterally rotate the hip, and also to extend the trunk.
Exercise and stretching
Any exercise that works and/or stretches the buttocks is suitable, for example lunges, hip thrusts, climbing stairs, fencing, bicycling, rowing, squats, arabesque, aerobics, and various specific exercises for the bottom.
Powerlifting exercises which are known to significantly strengthen the gluteal muscles include the squat, deadlift, leg press, feet in squats (chin on chest & stick glutes out) and good mornings (bend over with a bar on the shoulders with a light amount of weight).