Stabilizer type X36

Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 12 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,S4RF),
(T3IQ,S2F),
(T9IQ,S6R).
(T0,S0),
(T6,S4RF),
(T3IQ,S2R),
(T9IQ,S10F).
(T0,S0),
(T6,S4RF),
(T3IQ,S6F),
(T9IQ,S10R).
(T0,S0),
(T6,S4RF),
(T3IQ,S6R),
(T9IQ,S2F).
(T0,S0),
(T6,S4RF),
(T3IQ,S10F),
(T9IQ,S2R).
(T0,S0),
(T6,S4RF),
(T3IQ,S10R),
(T9IQ,S6F).
(T0,S0),
(T6,S10RF),
(T3IQ,R),
(T9IQ,S2F).
(T0,S0),
(T6,S10RF),
(T3IQ,S2F),
(T9IQ,R).
(T0,S0),
(T6,S10RF),
(T3IQ,S4R),
(T9IQ,S6F).
(T0,S0),
(T6,S10RF),
(T3IQ,S6F),
(T9IQ,S4R).
(T0,S0),
(T6,S10RF),
(T3IQ,S8R),
(T9IQ,S10F).
(T0,S0),
(T6,S10RF),
(T3IQ,S10F),
(T9IQ,S8R).

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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