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) .

Goto Database on tone rows and tropes
version 1.0

Stabilizer type X88

Stabilizer type X₈₈