17.60 (2010)

Given a set $\mathcal{P}$ of odd primes, let $\text{CT}_\mathcal{P}(\mathbb{Z})$ denote the subgroup of $\text{CT}(\mathbb{Z})$ (see 17.57) which is generated by all class transpositions which interchange residue classes whose moduli have only prime factors in $\mathcal{P} \cup \{2\}$. The groups $\text{CT}_\mathcal{P}(\mathbb{Z})$ are simple (Math. Z., 264, no. 4 (2010), 927–938). Are they pairwise nonisomorphic?