I'm thinking about the original Solomani battle-group; it should've had several capital ships, including at least one capital-scale troop carrier with a division (or more) of troops.
Before their arrival, the local worlds were settled in the recent centuries by various independent colonists from Imperial, Sword-Worlder and Zhodani origins, living mostly in low-tech colonies. When the Solomani arrived, they quickly took over a few of these worlds and began building a more advanced technological and industrial base.
The most highly-populated world (Subsector M 0305), originally settled by colonists from the Spinward Marches and called Asherah, became the NHC's capital and was renamed New Home. It was heavily industrialized and saw a population boom, rising from UWP D768873-7 to UWP A778935-D in the last century. It's atmosphere, however, became tainted with pollution; while it is not immediately poisonous to any visitor, prolonged exposure to it causes respiratory illness. Most residents live in sealed arcologies, with only the poorest living outside them in shanty-towns.
The New Home Confederation is, in theory, a presidential democracy, but in practice the real power rests in the hands of the Solomani naval officer caste. The Solomani who misjumped into this part of Foreven were, fortunately, led by relatively moderate officers (belonging to the HVD faction which sees all Humans, Vargar and Dolphins as Solomani), who had no problem accepting the locals as Solomani and trying to integrate the new arrivals with them (while, of course, retaining power in their own hands).
The Solomani Party still exists in the NHC, and the entire officer caste are Party members, but the actual power lies in the hands of the Naval High Command rather than the Party Secretariat. No other political parties are allowed, but factions within the Party are tolerated and even encouraged (with the HVD faction holding a majority in the Assembly). SolSec also exists in the NHC, but is far less powerful than back home in the Solomani Confederation.
Member worlds are encouraged to deal with local matters independently; the Naval High Command holds supreme power, of course, but the member worlds have a significant amount of autonomy in most fields other than military or (external) diplomatic matters.
The highest technology level, afforded mostly by the military and the larger corporations, is TL-D, but the majority of the civilian population has access to TL-B goods (and civilian starships). New Home holds the only shipyards in the subsector, capable of producing TL-D military ships and TL-B civilian craft.
The largest corporation in the NHC is Novastar Incorporated, manufacturing anything from robots through colonial supplies to civilian starships. Military equipment is manufactured by state-run companies.