They are distinct from the chlorosulfates, which have a chlorine atom attached to the sulfur as the ClSO3− anion.
As minerals they are included in the Nickel-Strunz classification group 7.DG.
The book Hey's Chemical Index of Minerals groups these in subgroup 12.2.
[dubious – discuss] Uniaxial (+) nω = 1.724 – 1.746 nε = 1.738 – 1.758 Birefringence: 0.026 Biaxial (+) Max birefringence: δ = 0.070 Biaxial (+) nα = 1.868 nβ = 1.892 nγ = 1.928 2V:measured: 80° Birefringence: 0.060
Max birefringence: δ = 0.023 2V: measured: 90° , calculated: 88° Max birefringence: δ = 0.022 Uniaxial (-) nω = 1.694 nε = 1.641 Max birefringence: δ = 0.053 Max birefringence: δ = 0.006 2V: calculated: 79° Max birefringence: δ = 0.005 2V: measured: 77° , calculated: 78° Max birefringence: δ = 0.092 Biaxial (-) nα = 1.462 nβ = 1.482 nγ = 1.495 2V: measured: 71° , calculated: 76° Max birefringence: δ = 0.033 2V: measured: 112° to 114°, calculated: 66° Max birefringence: δ = 0.022 Biaxial (+) nα = 1.695 nβ = 1.718 nγ = 1.759 2V: measured: 75° , calculated: 76° Max birefringence: δ = 0.064 Max birefringence: δ = 0.010 Max Birefringence: δ = 0.021 a = 15.882 Z=4 Biaxial (-) nα = 1.515(1) nβ = 1.540(1) nγ = 1.545(1) 2V: measured: 48°, calculated: 47.6° Max birefringence: δ = 0.030 Uniaxial (+) nω = 1.583 nε = 1.695 Max Birefringence:δ = 0.112 Max birefringence: δ = 0.002 Biaxial (+) nα = 1.920 nβ = 1.940 nγ = 1.950 Max birefringence: δ = 0.030 Biaxial nα = 2.120 nγ = 2.160 Max birefringence: δ = 0.040 Max birefringence: δ = 0.003 Max birefringence: δ = 0.008 Max birefringence: δ = 0.002 Biaxial nα = 2.140 nγ = 2.150 Max birefringence: δ = 0.010 Birefringence: δ = 0.017 Max birefringence: δ = 0.002 Max birefringence δ = 0.005 2V: measured: 63° to 77°, calculated: 76° Max birefringence: δ = 0.025 Uniaxial (-) nω = 1.536 nε = 1.510 Max birefringence: δ = 0.026 Max birefringence: δ = 0.015 Max birefringence: δ = 0.002 Max birefringence: δ = 0.005 Max birefringence:δ = 0.019 SO4:Cl Some "chloride sulfates" are sold as solutions in water and used for water treatment.