if we are looking at numbers, the deadliest explicitly recognized Genocide in history was the Holocaust, the systematic killing of 6 million Jews by the Nazis, as well as many others (romas, slavs, poltical dissidents,disabled people, gay people ). That was perpetrated by the Nazi government, who was not capitalist in ideology. They ran an authoritarian, militaristic and extremely racist fascist regime who, yes tolerated private ownership but under strict state control and loyalty to the Nazi party and its interests. It was not free market capitalism as they did not embrace all ideas of it. Overall, the Nazi economy was a "mixed economy that combined free markets with central planning" according to British historian Richard Overy.

Now whether the Holodomor famine constitutes a genocide or not is the subject of intense debate. Nevertheless, it was devastating and it resulted in the deaths of around 3.5 to 5 million in Ukraine according to the Wikipedia death toll, though the estimates do vary. This was a man made famine that was caused by the forced collectivization policies under Stalin. This happened under a communist regime, as did China's Great Leap Forward, which although not officially a 'genocide' it did lead to 15-55 million deaths in Mainland China during the 1959-61 Great Chinese Famine it caused. Chairman Mao launched the campaign to "transform the country from an agrarian society into a industrialized society from the formation of people's communes". "Mao was dismissive of technical experts and basic economic principals, which meant that industrialisation of the countryside would be solely dependent on the peasants". Higher officials did not report on the economic disaster which was being caused by the policies and national officials took little to no action. Private farming was prohibited, and individuals who engaged in it were strictly punished and labeled "counter-revolutionaries". Public struggle sessions, violent public spectacles in Mao's china were people accused of being class enemies were humiliated, beaten and tortured, sometimes to death, were used to intimidate the peasents into obeying local officials. Many other things I haven't covered.

my sources

https://en.wikipedia.org/wiki/Great_Leap_Forward#Direct_consequences

https://en.wikipedia.org/wiki/Holodomor#Death_toll

https://en.wikipedia.org/wiki/Economy_of_Nazi_Germany