(a) They’re not numbered; and
(b) Ragnarok.
@Elise No need to delete the posts like that; I needed a summary/pointer to figure out what you were referring to, but deletion makes it hard to track the conversation. Mind if I revert them?
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My bad. Is the formal organisational term just “fleet” then, and other fleet-sized but not org-charted collections of ships are just unusually large task forces?
I note in the glimpses of future history we have had, that the Republic never does try and tip over the game board before it loses and fragments quasi-peacefully. So, Ragnarok would be from some other frontier or something unpleasant boiling up from the non-plexus stars in the Worlds?
Thank you kindly for your consideration! 
“Fleet” means “top-level administrative grouping of ships” in IN jargon: Home Fleet, Capital Fleet, Merchancy Fleet, or one of the direction/location based Field Fleets.
If a fleet needs to create internal subdivisions for administrative purposes, that’s a flotilla. For strategic purposes, the hierarchy goes “Battle Fleet” - associated with a Theater Command (i.e., under a Warmain) or a Grand Admiral, and named accordingly, under which are task forces, etc..
(Major ones get names from the IN cryptonym generator; minor ones are numbered in accordance with the Too Damn Many Of These policy. Task groups and units get duodecimals of the parent task force.)
Ragnarok is, almost definitionally, an unknown unknown. The Admiralty has plans for the other three possibilities.
Also, I note, while you might have all of a Battle Fleet in one place, if it was in one place and doing the same thing it would also be a single Task Force, on the grounds that a task force is what you call a naval strategic unit and there’s no good reason to change that just because your battle fleet happens to have only one large task force in it right now. That would be silly.
Their specialities are really difficult to condensate in a few words. May you please read the Calibration part as a whole?
A quick question; Are the Clanks and Black Smoke the sole experimental technology Legion? Or are there others?
I’m imaging so-called Gemini Technis, the twin technologist Legions tracing their history to the dawn of Imperial civilisation, whose specialties somewhat overlapping and complementing each other. One are “curators”, the other are “reclaimers”, etc.
I mean, as far as I can tell, they’re psi-enhanced pattern-reading precognitive commandos, who mostly predict and nudge the way Transcendant soul shards do, occasionally taking the field to tip over a balance no one else even can imagine.
The key here is the psi-enhancement amplified by close-mesh cognition. And what I’m wondering is why that would be worth a specialized unit for the Imperial Navy. What is it that can’t be installed, uploaded, memewaved, or soul-shard nudged?
I think there’s at least a few of those?