A triumvirate is a group of three men. A duumvirate is a group of two.
The word is often used to mention a historical event or in talks of government. The word troika is Russian for triumvirate, and the term was used in the Soviet Union after V.I. Lenin died. Joseph Stalin, Lev Kamenev, and Grigory Zinoviev teamed up to gain power of the government. In the Soviet Union, troikas were usually considered to be three main people in the government: Party leader, head of state, and head of government.
In Ancient Rome, Julius Caesar was a member of the first triumvirate with Pompey and Crassus. In 43 B.C.E. after he was dead, Marc Antony, Marcus Lepidus, and Octavian formed a second triumvirate to rule the Roman Empire.