[GAP Forum] Metrics for large and small permutation groups.

[Javaid]

Dear Gap Forum,
 
I have difficulty with this somewhat informal terminology sometime used in the literature—“small groups” and “large groups”. 
My understanding is that the order of a permutation  group is at the most exponential in the degree of the group—more specifically n!, when the degree is n (which is true for all Symmetric groups).
 
So what is the interpretation of “large groups”? 
 
Thank you,
 
 
Javaid Aslam