Stabilizer type U10

Acting group: D12 × D12
There are exactly 18 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,S6),
(I,SR),
(T6I,S7R).
(T0,S0),
(T6,S6),
(I,S3R),
(T6I,S9R).
(T0,S0),
(T6,S6),
(I,S5R),
(T6I,S11R).
(T0,S0),
(T6,S6),
(I,S7R),
(T6I,SR).
(T0,S0),
(T6,S6),
(I,S9R),
(T6I,S3R).
(T0,S0),
(T6,S6),
(I,S11R),
(T6I,S5R).
(T0,S0),
(T6,S6),
(T2I,SR),
(T8I,S7R).
(T0,S0),
(T6,S6),
(T2I,S3R),
(T8I,S9R).
(T0,S0),
(T6,S6),
(T2I,S5R),
(T8I,S11R).
(T0,S0),
(T6,S6),
(T2I,S7R),
(T8I,SR).
(T0,S0),
(T6,S6),
(T2I,S9R),
(T8I,S3R).
(T0,S0),
(T6,S6),
(T2I,S11R),
(T8I,S5R).
(T0,S0),
(T6,S6),
(T4I,SR),
(T10I,S7R).
(T0,S0),
(T6,S6),
(T4I,S3R),
(T10I,S9R).
(T0,S0),
(T6,S6),
(T4I,S5R),
(T10I,S11R).
(T0,S0),
(T6,S6),
(T4I,S7R),
(T10I,SR).
(T0,S0),
(T6,S6),
(T4I,S9R),
(T10I,S3R).
(T0,S0),
(T6,S6),
(T4I,S11R),
(T10I,S5R).

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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