Stabilizer type W18

Acting group: Aff1(Z12) × D12
There are exactly 12 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,R),
(T3IQ,S6),
(T9IQ,S6R).
(T0,S0),
(T6,R),
(T3IQ,S6R),
(T9IQ,S6).
(T0,S0),
(T6,S2R),
(T3IQ,S6),
(T9IQ,S8R).
(T0,S0),
(T6,S2R),
(T3IQ,S8R),
(T9IQ,S6).
(T0,S0),
(T6,S4R),
(T3IQ,S6),
(T9IQ,S10R).
(T0,S0),
(T6,S4R),
(T3IQ,S10R),
(T9IQ,S6).
(T0,S0),
(T6,S6R),
(T3IQ,R),
(T9IQ,S6).
(T0,S0),
(T6,S6R),
(T3IQ,S6),
(T9IQ,R).
(T0,S0),
(T6,S8R),
(T3IQ,S2R),
(T9IQ,S6).
(T0,S0),
(T6,S8R),
(T3IQ,S6),
(T9IQ,S2R).
(T0,S0),
(T6,S10R),
(T3IQ,S4R),
(T9IQ,S6).
(T0,S0),
(T6,S10R),
(T3IQ,S6),
(T9IQ,S4R).

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) .

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