Stabilizer type U6

Acting group: D12 × D12
There are exactly 36 groups in this conjugacy class.
The group order is 2.
(T0,S0),
(TI,R).
(T0,S0),
(TI,S2R).
(T0,S0),
(TI,S4R).
(T0,S0),
(TI,S6R).
(T0,S0),
(TI,S8R).
(T0,S0),
(TI,S10R).
(T0,S0),
(T3I,R).
(T0,S0),
(T3I,S2R).
(T0,S0),
(T3I,S4R).
(T0,S0),
(T3I,S6R).
(T0,S0),
(T3I,S8R).
(T0,S0),
(T3I,S10R).
(T0,S0),
(T5I,R).
(T0,S0),
(T5I,S2R).
(T0,S0),
(T5I,S4R).
(T0,S0),
(T5I,S6R).
(T0,S0),
(T5I,S8R).
(T0,S0),
(T5I,S10R).
(T0,S0),
(T7I,R).
(T0,S0),
(T7I,S2R).
(T0,S0),
(T7I,S4R).
(T0,S0),
(T7I,S6R).
(T0,S0),
(T7I,S8R).
(T0,S0),
(T7I,S10R).
(T0,S0),
(T9I,R).
(T0,S0),
(T9I,S2R).
(T0,S0),
(T9I,S4R).
(T0,S0),
(T9I,S6R).
(T0,S0),
(T9I,S8R).
(T0,S0),
(T9I,S10R).
(T0,S0),
(T11I,R).
(T0,S0),
(T11I,S2R).
(T0,S0),
(T11I,S4R).
(T0,S0),
(T11I,S6R).
(T0,S0),
(T11I,S8R).
(T0,S0),
(T11I,S10R).

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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