  For simple twisted group algebra over a group $G$, if $G^{\shortmid}$ is Hall
subgroup of $G$ then the semi-center is simple. Simple twisted groups algebras
correspond to groups of central type. We classify all groups of central type of
order $p^4$ where $p$ is prime and use this to show that for odd primes $p$
there exists a unique group $G$ of order $p^4$ such that there exists simple
twisted group algebra over $G$ with a commutative semi-center. Moreover, if $1<
|G|< 64$, then the semi-center of simple twisted group algebras over $G$ is
non-commutative and this bounds are strict.
