From This Might Be A Wiki

El Grupo De Rock And Roll was the name John Flansburgh and John Linnell played under at their very first live show in August 1982. The show took place at a Sandinista rally in Central Park. According to the Early Years Handbook they were introduced this way because most of the people in attendance did not speak English, but Spanish as a primary language. The name roughly translates to The Rock and Roll Group. However, before their second show, the Johns changed their name to They Might Be Giants, taken indirectly from the title of the 1971 film, They Might Be Giants, which itself is a reference to Don Quixote.

In an interview with NY1, John Linnell explains that a friend from high school initially got them the gig. According to Linnell, "She immediately thought, 'Well, there's this coalition that's all celebrating the anniversary of the Sandinista Revolution, and they need a band.'" He added that it was their only Sandinsta rally to date.

There is one known photograph of the show, which was archived in the Dial-A-Song: 20 Years Of They Might Be Giants liner notes. In the photo, John Flansburgh appears to be playing a red, right-handed Gibson ES-330 (with the strings reversed to function as a lefty guitar), and Linnell is playing a Farfisa Compact organ.