Erdag and Deveci [13] defined the Padovan-Padovan p-sequence and they studied properties of this sequence. Then, Akuzum and Deveci [1] studied the Padovan-Padovan p-sequence modulo m . Also, they discussed the connections between the order the cyclic groups obtained and the periods of the Padovan-Padovan p-sequence according to modulo m . In this paper, we redefine the Padovan-Padovan p-sequence by means of the elements of the groups and then, we examine this sequence in the finite groups in detail. Also, we obtain the lengths of the periods of the Padovan-Padovan 4-sequence in the semidihedral group SD 2m as applications of the results obtained.