Integer group determinants of order 16

Abstract

Let \(\textrm{C}_{n}\) and \(\textrm{Q}_{n}\) denote the cyclic group and the generalized quaternion group of order n, respectively. We determine all possible values of the integer group determinants of \(\textrm{C}_{8} \rtimes _{3} \textrm{C}_{2}\) and \(\textrm{Q}_{8} \rtimes \textrm{C}_{2}\), which are the unresolved groups of order 16 (Serrano, Paudel and Pinner also obtained a complete description of the integer group determinants of \(\textrm{Q}_{8} \rtimes \textrm{C}_{2}\) independently of this paper and presented it a few days earlier than this paper). Also, we give a diagram of the set inclusion relations between the integer group determinants for all groups of order 16