So, while the revolution and war of independence was still ongoing they formed a government around Kádár, and when the Soviet intervetion begin they started a broadcast saying that Nagy Imre (the PM during the struggle, faithful communist himself, Muscowite but not part of the 5-man clique and had troubling social-democratic deviations) was weak and counter-revolutionaries sidetracked the reform movement. They are essentially labeled the revolution as a reactionary counter-revolution - since communists appropriated the term revolution - and said this is why they had to form a new government, and then this government asked the help of the Soviet comrades. On November 7th Kádár and his govt. arrived to Budapest. Fights were went on to the 11th.

The Reprisal was essentially a political murder spree in a legal coating.
Random executions basically started right after the new government came with the Red Army. During the revolution the political police, the AVH was abolished, members fled to the Soviet Union, and they came back, employed again in the state apparatus, mind set on revenge. The Red Army supported them, their local commander was a KGB general.
By 1957 March-April, the legal foundation was laid, but not by the legislation, but by the central committee of the party which issued statutes in the name of the government. They simplified the penal procedure, condensed it to the quickness of martial law. New judiciary bodies were set up entrusted with the retribution.
They were quite busy. They found 26-27 000 people guilty. 470 people got death penalty, 372 were executed by them (some execution were done outside the legal framework). Over 20 000 were sent to prison, and another 10-15 000 were gulaged. Over 200 000 people made the choice to emigrate.