The 79 Group was a leftist organisation committed to the idea that the SNP should be in favour of an independent Scotland being a socialist republic. The group was bolstered when many Scottish Labour Party (SLP) members decided to join the SNP after the collapse of the SLP. This made the SNP-left even stronger and they started to exert their influence in the party.
The SNP leadership however took a dim view of internal factions and in the early 1980s they proscribed the 79 Group, along with another internal SNP faction Siol nan Gaidheal. The 79 Group however reformed itself as a cross-party organisation in an attempt to carry on the work it had began, but this resulted in the expulsion from the SNP of many 79 Group leaders (including Alex Salmond who would later become the SNP leader).
The 79 Group leaders successfully appealed their expulsion and once back in the SNP many would go on to high office in the party, including the aforementioned Salmond, as well as Roseanna Cunningham and Kenny MacAskill.
Margo MacDonald was a high profile member of the 79 Group.