In French, to say that someone is the key element of the dynamic of a group, we can use the expression "she/he is the engine of the group" (Elle/Il est le moteur du groupe). This clearly shows that this person is what moves the group forward.
What would be a similar expression in English?
You could use:
He is the driving force behind/of the group.
"driving force" is similar to what an "engine" does, and I would prefer "behind" since he/she is pushing it along.
One expression that might work is:
He is the leader of the pack.
TFD defines “lead the pack* as:
To be at the forefront of a particular group, either literally or figuratively.
It’s a relatively common expression, much thanks to a hit song from the 1960s by the Shangri-Las.
It’s often used in sports journalism, when talking about leaders of teams. For example, one photo from the Boston Herald was captioned:
LEADER OF THE PACK: Julian Edelman holds court with the receivers group during the Pats’ OTA workout on Tuesday in Foxboro.
while a news story about a local high school wrestling team said:
Senior Joe Hackett is the leader of the pack. The returning district qualifier is a longtime wrestler who was unanimously named captain, and for good reason.
