Is every finite quasi-simple group generated by 2 elements ?


Recall that G is quasi-simple if G is perfect and G/Z(G) is simple.


Edit: If the answer is yes, do we know of a larger class of finite groups (beyond the finite quasi-simple groups) having the 2-generation property ?


Edited: Yes, there is another class. See my answers in comments.



Is every finite quasi-simple group generated by 2 elements?
It turns out the answer is Yes.


This is because G/Z(G) is simple and hence generated by 2 elemnts>
Moreover, if 2 elements generate a perfect group modulo its center, then they evidently generate the group since 


G = < a, b> Z(G) and G = [G, G]. 
imply G = < a, b>. That is, G is generated by a and b.


Moreover, G is "quasi-generated" by 1.5 elements in the sense that for all x 
in G - Z(G), there exists y in G, such that G =< x, y>. 


