Stabilizer type W'9

Acting group: D12 × Aff1(Z12)
There are exactly 2 groups in this conjugacy class.
The group order is 2.
(T0,S0),
(T6,S4RF).
(T0,S0),
(T6,S10RF).

Where
S=T=(1,2,3,4,5,6,7,8,9,10,11,12) ,
R=(6,7)(5,8)(4,9)(3,10)(2,11)(1,12) ,
I=(7)(6,8)(5,9)(4,10)(3,11)(2,12)(1) ,
F=Q=(10)(8,12)(7)(5,9)(4)(3,11)(2,6)(1) .

Goto Database on tone rows and tropes
version 1.0