The Minimal Degree Of The Permutation Representation Of Finite P-groups

Let G be a finite group. If there exists a positive integer d such that G<Sd but G< Sd-1, then d is called the minimal degree of the permutation representation of G. In this paper, we determined the minimal degree of the permutation representation of some finite p-groups, such as 2-groups of maximal class, finite p-groups of order≤ p4 and 2-groups of order 25.