The Einsatzgruppen were mobile killing units (death squads) that operated behind German lines on the Eastern Front. They were under the control of the SD, which was headed by Heydrich till his assassination in June 1942. Their main function was exterminating Jews. (Other units were used against guerrillas).
On September 29-30, 1941, the German Einsantzgruppen (a military division tasked with murdering Jews) killed 33,771 Jews in the third largest single massacre of Jews in the Holocaust. There were other "smaller" Einstazgruppen attacks on Jews in the same area as well.
Beginning on September 29, 1941 more than 33,000 Jews were marched in small groups to the Babi Yar ravine to the north of Kiev (Ukraine), ordered to strip naked, and then machine-gunned into the ravine by SD- Einsatzgruppe C, commanded by Dr. Dr. Otto Rasch. (He was called Dr. Dr. because he had two(!) doctorates).
mainly, he killed them in concentration camps, and ghettos, where in the ghettos, they got very sick, hungry,and starved to death. in the concentration camps, the soldiers there and guards there, worked, tortured and beat them to death.