Stabilizer type X88


Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 24 groups in this conjugacy class.
The group order is 24.
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,R),
(T3I,S2R),
(T5I,S4R),
(T7I,S6R),
(T9I,S8R),
(T11I,S10R),
(TQ,S5F),
(T3Q,S7F),
(T5Q,S9F),
(T7Q,S11F),
(T9Q,SF),
(T11Q,S3F),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,R),
(T3I,S2R),
(T5I,S4R),
(T7I,S6R),
(T9I,S8R),
(T11I,S10R),
(TQ,S11F),
(T3Q,SF),
(T5Q,S3F),
(T7Q,S5F),
(T9Q,S7F),
(T11Q,S9F),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S2R),
(T3I,S4R),
(T5I,S6R),
(T7I,S8R),
(T9I,S10R),
(T11I,R),
(TQ,SF),
(T3Q,S3F),
(T5Q,S5F),
(T7Q,S7F),
(T9Q,S9F),
(T11Q,S11F),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S2R),
(T3I,S4R),
(T5I,S6R),
(T7I,S8R),
(T9I,S10R),
(T11I,R),
(TQ,S7F),
(T3Q,S9F),
(T5Q,S11F),
(T7Q,SF),
(T9Q,S3F),
(T11Q,S5F),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S4R),
(T3I,S6R),
(T5I,S8R),
(T7I,S10R),
(T9I,R),
(T11I,S2R),
(TQ,S3F),
(T3Q,S5F),
(T5Q,S7F),
(T7Q,S9F),
(T9Q,S11F),
(T11Q,SF),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S4R),
(T3I,S6R),
(T5I,S8R),
(T7I,S10R),
(T9I,R),
(T11I,S2R),
(TQ,S9F),
(T3Q,S11F),
(T5Q,SF),
(T7Q,S3F),
(T9Q,S5F),
(T11Q,S7F),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S6R),
(T3I,S8R),
(T5I,S10R),
(T7I,R),
(T9I,S2R),
(T11I,S4R),
(TQ,S5F),
(T3Q,S7F),
(T5Q,S9F),
(T7Q,S11F),
(T9Q,SF),
(T11Q,S3F),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S6R),
(T3I,S8R),
(T5I,S10R),
(T7I,R),
(T9I,S2R),
(T11I,S4R),
(TQ,S11F),
(T3Q,SF),
(T5Q,S3F),
(T7Q,S5F),
(T9Q,S7F),
(T11Q,S9F),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S8R),
(T3I,S10R),
(T5I,R),
(T7I,S2R),
(T9I,S4R),
(T11I,S6R),
(TQ,SF),
(T3Q,S3F),
(T5Q,S5F),
(T7Q,S7F),
(T9Q,S9F),
(T11Q,S11F),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S8R),
(T3I,S10R),
(T5I,R),
(T7I,S2R),
(T9I,S4R),
(T11I,S6R),
(TQ,S7F),
(T3Q,S9F),
(T5Q,S11F),
(T7Q,SF),
(T9Q,S3F),
(T11Q,S5F),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S10R),
(T3I,R),
(T5I,S2R),
(T7I,S4R),
(T9I,S6R),
(T11I,S8R),
(TQ,S3F),
(T3Q,S5F),
(T5Q,S7F),
(T7Q,S9F),
(T9Q,S11F),
(T11Q,SF),
(IQ,S7RF),
(T2IQ,S9RF),
(T4IQ,S11RF),
(T6IQ,SRF),
(T8IQ,S3RF),
(T10IQ,S5RF).
(T0,S0),
(T2,S2),
(T4,S4),
(T6,S6),
(T8,S8),
(T10,S10),
(TI,S10R),
(T3I,R),
(T5I,S2R),
(T7I,S4R),
(T9I,S6R),
(T11I,S8R),
(TQ,S9F),
(T3Q,S11F),
(T5Q,SF),
(T7Q,S3F),
(T9Q,S5F),
(T11Q,S7F),
(IQ,SRF),
(T2IQ,S3RF),
(T4IQ,S5RF),
(T6IQ,S7RF),
(T8IQ,S9RF),
(T10IQ,S11RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,R),
(T3I,S10R),
(T5I,S8R),
(T7I,S6R),
(T9I,S4R),
(T11I,S2R),
(TQ,S5F),
(T3Q,S3F),
(T5Q,SF),
(T7Q,S11F),
(T9Q,S9F),
(T11Q,S7F),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,R),
(T3I,S10R),
(T5I,S8R),
(T7I,S6R),
(T9I,S4R),
(T11I,S2R),
(TQ,S11F),
(T3Q,S9F),
(T5Q,S7F),
(T7Q,S5F),
(T9Q,S3F),
(T11Q,SF),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S2R),
(T3I,R),
(T5I,S10R),
(T7I,S8R),
(T9I,S6R),
(T11I,S4R),
(TQ,SF),
(T3Q,S11F),
(T5Q,S9F),
(T7Q,S7F),
(T9Q,S5F),
(T11Q,S3F),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S2R),
(T3I,R),
(T5I,S10R),
(T7I,S8R),
(T9I,S6R),
(T11I,S4R),
(TQ,S7F),
(T3Q,S5F),
(T5Q,S3F),
(T7Q,SF),
(T9Q,S11F),
(T11Q,S9F),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S4R),
(T3I,S2R),
(T5I,R),
(T7I,S10R),
(T9I,S8R),
(T11I,S6R),
(TQ,S3F),
(T3Q,SF),
(T5Q,S11F),
(T7Q,S9F),
(T9Q,S7F),
(T11Q,S5F),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S4R),
(T3I,S2R),
(T5I,R),
(T7I,S10R),
(T9I,S8R),
(T11I,S6R),
(TQ,S9F),
(T3Q,S7F),
(T5Q,S5F),
(T7Q,S3F),
(T9Q,SF),
(T11Q,S11F),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S6R),
(T3I,S4R),
(T5I,S2R),
(T7I,R),
(T9I,S10R),
(T11I,S8R),
(TQ,S5F),
(T3Q,S3F),
(T5Q,SF),
(T7Q,S11F),
(T9Q,S9F),
(T11Q,S7F),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S6R),
(T3I,S4R),
(T5I,S2R),
(T7I,R),
(T9I,S10R),
(T11I,S8R),
(TQ,S11F),
(T3Q,S9F),
(T5Q,S7F),
(T7Q,S5F),
(T9Q,S3F),
(T11Q,SF),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S8R),
(T3I,S6R),
(T5I,S4R),
(T7I,S2R),
(T9I,R),
(T11I,S10R),
(TQ,SF),
(T3Q,S11F),
(T5Q,S9F),
(T7Q,S7F),
(T9Q,S5F),
(T11Q,S3F),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S8R),
(T3I,S6R),
(T5I,S4R),
(T7I,S2R),
(T9I,R),
(T11I,S10R),
(TQ,S7F),
(T3Q,S5F),
(T5Q,S3F),
(T7Q,SF),
(T9Q,S11F),
(T11Q,S9F),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S10R),
(T3I,S8R),
(T5I,S6R),
(T7I,S4R),
(T9I,S2R),
(T11I,R),
(TQ,S3F),
(T3Q,SF),
(T5Q,S11F),
(T7Q,S9F),
(T9Q,S7F),
(T11Q,S5F),
(IQ,S7RF),
(T2IQ,S5RF),
(T4IQ,S3RF),
(T6IQ,SRF),
(T8IQ,S11RF),
(T10IQ,S9RF).
(T0,S0),
(T2,S10),
(T4,S8),
(T6,S6),
(T8,S4),
(T10,S2),
(TI,S10R),
(T3I,S8R),
(T5I,S6R),
(T7I,S4R),
(T9I,S2R),
(T11I,R),
(TQ,S9F),
(T3Q,S7F),
(T5Q,S5F),
(T7Q,S3F),
(T9Q,SF),
(T11Q,S11F),
(IQ,SRF),
(T2IQ,S11RF),
(T4IQ,S9RF),
(T6IQ,S7RF),
(T8IQ,S5RF),
(T10IQ,S3RF).

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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