This is the best answer for this question: the SS got their fame because they were brutal. This is what was invented or rather exaggerated by the world. They were the ones who committed the most atrocities of World War II.
SS was not an ordinary group of the German army. They were the military branch of the Nazi Party. Hitler developed them as his security men and to impose his ideology, therefore, their whole operation was connected with Nazism concept of race and terror.
The best way to show their brutality is that they operated the whole holocaust. The SS planned it and ran the camps and deployed their personnel in every concentration and extermination camp location. Thus, they had killed approximately six and half million Jews and millions of other individuals who were not liked by the Nazis included the perons who were not in good health and shape.
There were also special units within the SS that were known as Einsatzgruppen. They were traveling assassination teams which killed more than a million people behind the front lines, way before the gas chambers were operational.
The war crimes were even more infamous with the regular SS soldiers who fought in them, the Waffen-SS. They also used to execute prisoners of war and kill civilians when they were able to capture towns. They exhibited worse behavior as compared to the regular German army.
All this evidence were shown in the courts after the war and the whole SS was officially declared as a criminal organization.
This was not a collection of random ill episodes, this was a planned, structured murder campaign of the extraordinary scale a genocide. Their reputation of brutality is quite reasonable.
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