What is the name of the group who sang the song of the fifties called sh-boom?

I believe it was the Elgins.

AnswerI believe it WA The Elgins

The song was written by members of The Chords, who recorded it for the Cat Label:Early March '54 it went to #2, R&B and ~9 in the Pop chart.

A few months later The Crewcuts waxed it( for Mercury) and it went to #1 staying there August thru' September, it charted for a total of 20 weeks.