Stabilizer type W14

Acting group: Aff1(Z12) × D12
There are exactly 18 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,S6),
(TI,R),
(T7I,S6R).
(T0,S0),
(T6,S6),
(TI,S2R),
(T7I,S8R).
(T0,S0),
(T6,S6),
(TI,S4R),
(T7I,S10R).
(T0,S0),
(T6,S6),
(TI,S6R),
(T7I,R).
(T0,S0),
(T6,S6),
(TI,S8R),
(T7I,S2R).
(T0,S0),
(T6,S6),
(TI,S10R),
(T7I,S4R).
(T0,S0),
(T6,S6),
(T3I,R),
(T9I,S6R).
(T0,S0),
(T6,S6),
(T3I,S2R),
(T9I,S8R).
(T0,S0),
(T6,S6),
(T3I,S4R),
(T9I,S10R).
(T0,S0),
(T6,S6),
(T3I,S6R),
(T9I,R).
(T0,S0),
(T6,S6),
(T3I,S8R),
(T9I,S2R).
(T0,S0),
(T6,S6),
(T3I,S10R),
(T9I,S4R).
(T0,S0),
(T6,S6),
(T5I,R),
(T11I,S6R).
(T0,S0),
(T6,S6),
(T5I,S2R),
(T11I,S8R).
(T0,S0),
(T6,S6),
(T5I,S4R),
(T11I,S10R).
(T0,S0),
(T6,S6),
(T5I,S6R),
(T11I,R).
(T0,S0),
(T6,S6),
(T5I,S8R),
(T11I,S2R).
(T0,S0),
(T6,S6),
(T5I,S10R),
(T11I,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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