In mathematics, a quasisimple group is a group that is a perfect central extension E of a simple group S. In other words, there is a short exact sequence 1 → Z → E → S → 1 {\displaystyle 1\to Z\to E\to S\to 1} such that E = [ E, E ] {\displaystyle E=[E,E]}, where Z {\displaystyle Z} denotes the center of E and [, ] denotes the commutator. Wikipedia