[soVeryTired]

I thought the work on the structure of DNA used Fourier analysis more than group theory.

I know harmonic analysis in general combines the two, but I'm sure Crick and Watson could have done their work without knowing the definition of a group.

[adw]

And by Crick and Watson you mean Crick, Watson, Franklin and Wilkins, right? It's fairly clear all four deserve at least partial authorship by modern standards. James Watson was a piece of work.

(https://www.theguardian.com/science/2015/jun/23/sexism-in-sc...)

Crick was absolutely certainly familiar with the crystallographic space groups; he was the student of Lawrence Bragg (https://en.wikipedia.org/wiki/Lawrence_Bragg), who is the youngest ever Nobel laureate in physics – winning it with his father for more or less inventing X-ray crystallography. It's mostly 19th-century mathematics, after all.