The most unusual of the criminal groups vying for world domination, Geese Howard's Southtown Syndicate is like its rivals in many ways, and different in others. The first major difference is that there are really two distinct parts of the Syndicate. The first is the criminal cartel part of it, and the second is a collection of legitimate businesses owned by Geese, collectively known as Howard Enterprises.
Geese owns the law in Southtown, and is probably the wealthiest person on the planet. While Howard Enterprises doesn't own every single business around, it's very likely your character owns at least one thing that was made by a company Geese owns. To most of the public, Geese is a respected businessman, a leader in his community, and widely regarded as an excellent martial artist.
If only the public knew. But they won't know anytime in the foreseeable future, since Geese also controls the news in Southtown, as well as most political figures there. Some law enforcement agencies know Geese is one of the most powerful crimelords on the planet, but they can't prove it to the world at large, and so he remains a free man with a generally good reputation.
Having talented fighters, money, and a large army of 'thugs', the Syndicate is a very powerful organization; only Shadaloo is more powerful, and only then in regards to a straight-out fight between massive groups. And the Syndicate is the most active group in many criminal venues, such as assassination-for-hire, kidnapping, slavery, and they nearly equal "R" in drug/weapon smuggling. The Syndicate is basically the Yakuza on a global scale, and indeed they have replaced/absorbed the Yakuza in Japan.
Of course, they also have a huge amount of enemies. Gedo High, while unaware that Geese Howard runs the organized crime scene in Southtown, nonetheless frequently clashes with Syndicate forces, often getting a bad reputation due to how the local media presents their activities with Geese's distinct spin on it.
Shadaloo is their direct rival, and Syndicate/Shadaloo battles are common; Shadaloo forces may raid a drug shipment of the Syndicate's, the Syndicate may torch one of Shadaloo's outpost bases, etc.; it's a back and forth 'shadow war' between these two.
Then there's Justice High. While not a direct combative threat to the Syndicate most of the time, Justice High's stated ideals clash strongly with Geese's method of operation. In a world run by Justice High graduates, it would be difficult to bribe government officials, since they would be "Super-Elites" with a strong sense of morals. The Syndicate would collapse. As a result, Geese monitors Justice High very carefully, since they represent a long-term threat to his plans...even if they don't realize it. Of course, there's always the chance that subversion, be it the Darkside Student Congress' or otherwise, could foil Justice High for good.
Finally, Geese has made enemies of a few families here and there. Terry and Andy Bogard, as well as their friends, know full well Geese is a crimelord and they have absolutely no love for him; they try to foil his activities when they can. Likewise, the Sakazakis know Geese runs the Syndicate, as Geese was the one who blackmailed Takuma into working as a Syndicate enforcer under the alias "Mr. Karate", and it's likely that Takuma has shared the information he has on the criminal underworld with family friends, such as King, Saishu Kusanagi, and so forth.