The death penalty does exist in Serilaq. It is used as punishment for murder, treason, and rape.
Method is a 3-member firing squad using 30-06 semi-automatic rifles. A checker then walks up to the condemned to check if he/she is actually dead. If not, the checker then draws a 9-mm. pistol and shoots the prisoner in the head.
Serilaq being only slightly over a year old as a country, it has yet to execute anybody charged with these crimes.