I got confused whether the center of semi dihedral group $SD_{24}$ is just ${e,a^6}$ or ${e,a^3,a^6,a^9}$ since all of elements are commute and it also equals to its inverse.
My definition for semi dihedral group:
$$SD_{8n}=\langle a,b\mid a^{4n}=b^2=1,bab=a^{2n-1}\rangle, $$
where $n\geq2$.