Erdös–Ko–Rado properties of some finite groups

Let $G$ be a subgroup of the symmetric group $\mathrm{Sym}(n)$ and $A$ be a subset of $G$. The subset $A$ is said to be intersecting if for any pair of permutations $\sigma, \tau \in A$ there exists $i, 1 \leq i \leq n,$ such that $\sigma(i)=\tau(i)$. The group $G$ has Erdös-Ko-Rado (EKR) property, if the size of any intersecting subset of $G$ is bounded above by the size of a point stabilizer in $G$. The group $G$ has the strict EKR property if every intersecting set of maximum size is the coset of the stabilizer of a point. The aim of this paper is to investigate the EKR and strict EKR properties of the groups $V_{8n}, U_{6n}, T_{4n}$ and $SD_{8n}$.