Let $\ G\ $ be a finite group with $\ |G|=n\ $
Caley's theorem states that $\ G\ $ is isomorphic to a subgroup of the symmetric group $\ S_n\ $
However, in many cases, the smallest positive integer $\ m\ $, such that $\ G\ $ is isomorphic to a subgroup of $\ S_m\ $ is smaller than $\ n\ $.
How can I determine $\ m\ $ , if I do not have access to GAP ?
Is there some applet or online calculator that can do this ? Or can $\ m\ $ be calculated by knowing specific properties of $\ G \ $ ?