Integer group determinants for abelian groups of order 16

Abstract

For any positive integer $n$, let ${\mathrm{C}}_n$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of ${\mathrm{C}}_4\times {\mathrm{C}}_2^2$, which is the only unsolved abelian group of order $16$.