I know "faction" is more common than "fraction" but I've found "fraction" as well in the Oxford Dictionary with similar meaning:
2.1 A dissenting group within a larger one. ‘the dominant classes or fractions in capitalist societies’
I though it could be a better choice in this case, but I might go back to using "faction" if "fraction" sounds weird to you.
The CGT is a trade-union central.
My question is about the best way of organising the sentence after "divided into".
"divided into an official and a dissenting faction"
"divided into an official faction and a dissenting one"
I could not find any other reference to "fraction" used as you describe. It may be "correct" but it is sufficiently rare and obscure that I would definitely avoid using it. My guess is that 99 out of 100 people will assume you made an English language beginner's error.
The CGT, divided into an official and a dissenting fraction, was reunited. (This reads OK for me.) The CGT, divided into an official fraction and a dissenting one, was reunited. (OK, but a bit awkward sounding to me.)
(I prefer the slightly modified version below to either of the above.)
The CGT, once divided into an official faction and a disssenting one, was reunited.
"once" = "at one time" and "at one time" can be substituted for "once".