Stabilizer type Y67

Acting group: 𝔄12
There are exactly 24 groups in this conjugacy class.
The group order is 8.
(T0,S0),
(T3,SF),
(T6,S6),
(T9,S7F),
(IQ,SRF),
(T3IQ,S2R),
(T6IQ,S7RF),
(T9IQ,S8R).
(T0,S0),
(T3,SF),
(T6,S6),
(T9,S7F),
(IQ,S7RF),
(T3IQ,S8R),
(T6IQ,SRF),
(T9IQ,S2R).
(T0,S0),
(T3,S3F),
(T6,S6),
(T9,S9F),
(IQ,SRF),
(T3IQ,S4R),
(T6IQ,S7RF),
(T9IQ,S10R).
(T0,S0),
(T3,S3F),
(T6,S6),
(T9,S9F),
(IQ,S7RF),
(T3IQ,S10R),
(T6IQ,SRF),
(T9IQ,S4R).
(T0,S0),
(T3,S5F),
(T6,S6),
(T9,S11F),
(IQ,SRF),
(T3IQ,S6R),
(T6IQ,S7RF),
(T9IQ,R).
(T0,S0),
(T3,S5F),
(T6,S6),
(T9,S11F),
(IQ,S7RF),
(T3IQ,R),
(T6IQ,SRF),
(T9IQ,S6R).
(T0,S0),
(T3,S7F),
(T6,S6),
(T9,SF),
(IQ,SRF),
(T3IQ,S8R),
(T6IQ,S7RF),
(T9IQ,S2R).
(T0,S0),
(T3,S7F),
(T6,S6),
(T9,SF),
(IQ,S7RF),
(T3IQ,S2R),
(T6IQ,SRF),
(T9IQ,S8R).
(T0,S0),
(T3,S9F),
(T6,S6),
(T9,S3F),
(IQ,SRF),
(T3IQ,S10R),
(T6IQ,S7RF),
(T9IQ,S4R).
(T0,S0),
(T3,S9F),
(T6,S6),
(T9,S3F),
(IQ,S7RF),
(T3IQ,S4R),
(T6IQ,SRF),
(T9IQ,S10R).
(T0,S0),
(T3,S11F),
(T6,S6),
(T9,S5F),
(IQ,SRF),
(T3IQ,R),
(T6IQ,S7RF),
(T9IQ,S6R).
(T0,S0),
(T3,S11F),
(T6,S6),
(T9,S5F),
(IQ,S7RF),
(T3IQ,S6R),
(T6IQ,SRF),
(T9IQ,R).
(T0,S0),
(T6,S6),
(TI,S4RF),
(T7I,S10RF),
(TQ,S3),
(T7Q,S9),
(IQ,SRF),
(T6IQ,S7RF).
(T0,S0),
(T6,S6),
(TI,S4RF),
(T7I,S10RF),
(TQ,S9),
(T7Q,S3),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(TI,S10RF),
(T7I,S4RF),
(TQ,S3),
(T7Q,S9),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(TI,S10RF),
(T7I,S4RF),
(TQ,S9),
(T7Q,S3),
(IQ,SRF),
(T6IQ,S7RF).
(T0,S0),
(T6,S6),
(T3I,S4RF),
(T9I,S10RF),
(T3Q,S3),
(T9Q,S9),
(IQ,SRF),
(T6IQ,S7RF).
(T0,S0),
(T6,S6),
(T3I,S4RF),
(T9I,S10RF),
(T3Q,S9),
(T9Q,S3),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(T3I,S10RF),
(T9I,S4RF),
(T3Q,S3),
(T9Q,S9),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(T3I,S10RF),
(T9I,S4RF),
(T3Q,S9),
(T9Q,S3),
(IQ,SRF),
(T6IQ,S7RF).
(T0,S0),
(T6,S6),
(T5I,S4RF),
(T11I,S10RF),
(T5Q,S3),
(T11Q,S9),
(IQ,SRF),
(T6IQ,S7RF).
(T0,S0),
(T6,S6),
(T5I,S4RF),
(T11I,S10RF),
(T5Q,S9),
(T11Q,S3),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(T5I,S10RF),
(T11I,S4RF),
(T5Q,S3),
(T11Q,S9),
(IQ,S7RF),
(T6IQ,SRF).
(T0,S0),
(T6,S6),
(T5I,S10RF),
(T11I,S4RF),
(T5Q,S9),
(T11Q,S3),
(IQ,SRF),
(T6IQ,S7RF).

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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