Stabilizer type X51

Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 9 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,S2F),
(Q,S8F),
(T6Q,S6).
(T0,S0),
(T6,S2F),
(T2Q,S6),
(T8Q,S8F).
(T0,S0),
(T6,S2F),
(T4Q,S8F),
(T10Q,S6).
(T0,S0),
(T6,S6F),
(Q,F),
(T6Q,S6).
(T0,S0),
(T6,S6F),
(T2Q,S6),
(T8Q,F).
(T0,S0),
(T6,S6F),
(T4Q,F),
(T10Q,S6).
(T0,S0),
(T6,S10F),
(Q,S4F),
(T6Q,S6).
(T0,S0),
(T6,S10F),
(T2Q,S6),
(T8Q,S4F).
(T0,S0),
(T6,S10F),
(T4Q,S4F),
(T10Q,S6).

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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