Stabilizer type W19

Acting group: Aff1(Z12) × D12
There are exactly 6 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T6,S6),
(TQ,S3),
(T7Q,S9).
(T0,S0),
(T6,S6),
(TQ,S9),
(T7Q,S3).
(T0,S0),
(T6,S6),
(T3Q,S3),
(T9Q,S9).
(T0,S0),
(T6,S6),
(T3Q,S9),
(T9Q,S3).
(T0,S0),
(T6,S6),
(T5Q,S3),
(T11Q,S9).
(T0,S0),
(T6,S6),
(T5Q,S9),
(T11Q,S3).

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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