Stabilizer type X80

Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 18 groups in this conjugacy class.
The group order is 8.
(T0,S0),
(T3,SF),
(T6,S6),
(T9,S7F),
(Q,S4F),
(T3Q,S9),
(T6Q,S10F),
(T9Q,S3).
(T0,S0),
(T3,SF),
(T6,S6),
(T9,S7F),
(TQ,S3),
(T4Q,S4F),
(T7Q,S9),
(T10Q,S10F).
(T0,S0),
(T3,SF),
(T6,S6),
(T9,S7F),
(T2Q,S10F),
(T5Q,S3),
(T8Q,S4F),
(T11Q,S9).
(T0,S0),
(T3,S3F),
(T6,S6),
(T9,S9F),
(Q,F),
(T3Q,S3),
(T6Q,S6F),
(T9Q,S9).
(T0,S0),
(T3,S3F),
(T6,S6),
(T9,S9F),
(TQ,S9),
(T4Q,F),
(T7Q,S3),
(T10Q,S6F).
(T0,S0),
(T3,S3F),
(T6,S6),
(T9,S9F),
(T2Q,S6F),
(T5Q,S9),
(T8Q,F),
(T11Q,S3).
(T0,S0),
(T3,S5F),
(T6,S6),
(T9,S11F),
(Q,S8F),
(T3Q,S9),
(T6Q,S2F),
(T9Q,S3).
(T0,S0),
(T3,S5F),
(T6,S6),
(T9,S11F),
(TQ,S3),
(T4Q,S8F),
(T7Q,S9),
(T10Q,S2F).
(T0,S0),
(T3,S5F),
(T6,S6),
(T9,S11F),
(T2Q,S2F),
(T5Q,S3),
(T8Q,S8F),
(T11Q,S9).
(T0,S0),
(T3,S7F),
(T6,S6),
(T9,SF),
(Q,S4F),
(T3Q,S3),
(T6Q,S10F),
(T9Q,S9).
(T0,S0),
(T3,S7F),
(T6,S6),
(T9,SF),
(TQ,S9),
(T4Q,S4F),
(T7Q,S3),
(T10Q,S10F).
(T0,S0),
(T3,S7F),
(T6,S6),
(T9,SF),
(T2Q,S10F),
(T5Q,S9),
(T8Q,S4F),
(T11Q,S3).
(T0,S0),
(T3,S9F),
(T6,S6),
(T9,S3F),
(Q,F),
(T3Q,S9),
(T6Q,S6F),
(T9Q,S3).
(T0,S0),
(T3,S9F),
(T6,S6),
(T9,S3F),
(TQ,S3),
(T4Q,F),
(T7Q,S9),
(T10Q,S6F).
(T0,S0),
(T3,S9F),
(T6,S6),
(T9,S3F),
(T2Q,S6F),
(T5Q,S3),
(T8Q,F),
(T11Q,S9).
(T0,S0),
(T3,S11F),
(T6,S6),
(T9,S5F),
(Q,S8F),
(T3Q,S3),
(T6Q,S2F),
(T9Q,S9).
(T0,S0),
(T3,S11F),
(T6,S6),
(T9,S5F),
(TQ,S9),
(T4Q,S8F),
(T7Q,S3),
(T10Q,S2F).
(T0,S0),
(T3,S11F),
(T6,S6),
(T9,S5F),
(T2Q,S2F),
(T5Q,S9),
(T8Q,S8F),
(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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