Stabilizer type X78

Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 36 groups in this conjugacy class.
The group order is 8.
(T0,S0),
(T6,S6),
(I,SR),
(T6I,S7R),
(T3Q,S3),
(T9Q,S9),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(I,SR),
(T6I,S7R),
(T3Q,S9),
(T9Q,S3),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(I,S3R),
(T6I,S9R),
(T3Q,S3),
(T9Q,S9),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(I,S3R),
(T6I,S9R),
(T3Q,S9),
(T9Q,S3),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(I,S5R),
(T6I,S11R),
(T3Q,S3),
(T9Q,S9),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(I,S5R),
(T6I,S11R),
(T3Q,S9),
(T9Q,S3),
(T3IQ,S2R),
(T9IQ,S8R).
(T0,S0),
(T6,S6),
(I,S7R),
(T6I,SR),
(T3Q,S3),
(T9Q,S9),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(I,S7R),
(T6I,SR),
(T3Q,S9),
(T9Q,S3),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(I,S9R),
(T6I,S3R),
(T3Q,S3),
(T9Q,S9),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(I,S9R),
(T6I,S3R),
(T3Q,S9),
(T9Q,S3),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(I,S11R),
(T6I,S5R),
(T3Q,S3),
(T9Q,S9),
(T3IQ,S2R),
(T9IQ,S8R).
(T0,S0),
(T6,S6),
(I,S11R),
(T6I,S5R),
(T3Q,S9),
(T9Q,S3),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(T2I,SR),
(T8I,S7R),
(T5Q,S3),
(T11Q,S9),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(T2I,SR),
(T8I,S7R),
(T5Q,S9),
(T11Q,S3),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(T2I,S3R),
(T8I,S9R),
(T5Q,S3),
(T11Q,S9),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(T2I,S3R),
(T8I,S9R),
(T5Q,S9),
(T11Q,S3),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(T2I,S5R),
(T8I,S11R),
(T5Q,S3),
(T11Q,S9),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(T2I,S5R),
(T8I,S11R),
(T5Q,S9),
(T11Q,S3),
(T3IQ,S2R),
(T9IQ,S8R).
(T0,S0),
(T6,S6),
(T2I,S7R),
(T8I,SR),
(T5Q,S3),
(T11Q,S9),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(T2I,S7R),
(T8I,SR),
(T5Q,S9),
(T11Q,S3),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(T2I,S9R),
(T8I,S3R),
(T5Q,S3),
(T11Q,S9),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(T2I,S9R),
(T8I,S3R),
(T5Q,S9),
(T11Q,S3),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(T2I,S11R),
(T8I,S5R),
(T5Q,S3),
(T11Q,S9),
(T3IQ,S2R),
(T9IQ,S8R).
(T0,S0),
(T6,S6),
(T2I,S11R),
(T8I,S5R),
(T5Q,S9),
(T11Q,S3),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(T4I,SR),
(T10I,S7R),
(TQ,S3),
(T7Q,S9),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(T4I,SR),
(T10I,S7R),
(TQ,S9),
(T7Q,S3),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(T4I,S3R),
(T10I,S9R),
(TQ,S3),
(T7Q,S9),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(T4I,S3R),
(T10I,S9R),
(TQ,S9),
(T7Q,S3),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(T4I,S5R),
(T10I,S11R),
(TQ,S3),
(T7Q,S9),
(T3IQ,S2R),
(T9IQ,S8R).
(T0,S0),
(T6,S6),
(T4I,S5R),
(T10I,S11R),
(TQ,S9),
(T7Q,S3),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(T4I,S7R),
(T10I,SR),
(TQ,S3),
(T7Q,S9),
(T3IQ,S4R),
(T9IQ,S10R).
(T0,S0),
(T6,S6),
(T4I,S7R),
(T10I,SR),
(TQ,S9),
(T7Q,S3),
(T3IQ,S10R),
(T9IQ,S4R).
(T0,S0),
(T6,S6),
(T4I,S9R),
(T10I,S3R),
(TQ,S3),
(T7Q,S9),
(T3IQ,S6R),
(T9IQ,R).
(T0,S0),
(T6,S6),
(T4I,S9R),
(T10I,S3R),
(TQ,S9),
(T7Q,S3),
(T3IQ,R),
(T9IQ,S6R).
(T0,S0),
(T6,S6),
(T4I,S11R),
(T10I,S5R),
(TQ,S3),
(T7Q,S9),
(T3IQ,S8R),
(T9IQ,S2R).
(T0,S0),
(T6,S6),
(T4I,S11R),
(T10I,S5R),
(TQ,S9),
(T7Q,S3),
(T3IQ,S2R),
(T9IQ,S8R).

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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