Caligula was the son of Germanicus and Vispania Agrippina. Vispania Aggripina was the daughter of Agrippa and Julia. Julia was Augustus’s daughter. So, Augustus is Caligula’s great-grandfather maternally.
Now, Germanicus (Caligula’s father) was the son of Nero Claudius Drusus and Antonia. Nero Claudius Drusus was the son of Livia Drusilla by her first husband, and is Augustus’s step-son. So, Augustus is Caligula’s step-great grandfather paternally.
Hey, it’s been several lifetimes since I’ve used that calender . I keep forgeting that subtractice numerals (IV in lieu of IIII) weren’t used 'till the Middle Ages. And the Romans didn’t use “A.U.C” that much either; they named the year for the 2 Consuls.