Similar to ⭐Princette♥PengthuluWrites 's suggestions, I'd think about some characteristics of the group.

How many people in the group?
Average age? Age range?
Why are they coming after your character?
Are there any limits or will they stop at nothing? Will they break laws and taboos?
How far will they go to maintain their anonymity?
Do the members of the group know each other?
How does the group communicate?
Do all the members of the group have similar backgrounds, eg. criminals, ex-military, etc.?
How well financed is the group? What access to technology or insider knowledge do they have?
Does the group have a timeline or time limit they have to stick to or get to your character within?

That's all I can come up with for now!

** Animated Images For Use By Premium+ Only **