In this study, we study the complex-type Pell p-numbers modulo m and further we get the periods and the ranks of the complex-type Pell p-numbers modulo m. Additionally, we give some results on the periods and the ranks of the complex-type Pell p-numbers modulo m. Then, we consider the multiplicative orders of the complex-type Pell p-matrix when read modulo m. Also, we redefine the complex-type Pell p-numbers by means of the elements of groups. Finally, we produce the periods of the complex-type Pell 2-numbers in the semidihedral group SD 2m, (m ≥ 4).