Stabilizer type X₈₃

Acting group: Aff₁(Z₁₂) × Aff₁(Z₁₂)
There are exactly 24 groups in this conjugacy class.
The group order is 12.

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S²F),
(T⁵I,S⁶F),
(T⁹I,S¹⁰F),
(T²Q,S⁴R),
(T⁶Q,S⁸R),
(T¹⁰Q,R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S²RF),
(T¹¹IQ,S⁶RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S²F),
(T⁵I,S⁶F),
(T⁹I,S¹⁰F),
(T²Q,S¹⁰R),
(T⁶Q,S²R),
(T¹⁰Q,S⁶R),
(T³IQ,S⁴RF),
(T⁷IQ,S⁸RF),
(T¹¹IQ,RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S⁶F),
(T⁵I,S¹⁰F),
(T⁹I,S²F),
(T²Q,S²R),
(T⁶Q,S⁶R),
(T¹⁰Q,S¹⁰R),
(T³IQ,S⁴RF),
(T⁷IQ,S⁸RF),
(T¹¹IQ,RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S⁶F),
(T⁵I,S¹⁰F),
(T⁹I,S²F),
(T²Q,S⁸R),
(T⁶Q,R),
(T¹⁰Q,S⁴R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S²RF),
(T¹¹IQ,S⁶RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S¹⁰F),
(T⁵I,S²F),
(T⁹I,S⁶F),
(T²Q,R),
(T⁶Q,S⁴R),
(T¹⁰Q,S⁸R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S²RF),
(T¹¹IQ,S⁶RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(TI,S¹⁰F),
(T⁵I,S²F),
(T⁹I,S⁶F),
(T²Q,S⁶R),
(T⁶Q,S¹⁰R),
(T¹⁰Q,S²R),
(T³IQ,S⁴RF),
(T⁷IQ,S⁸RF),
(T¹¹IQ,RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S²F),
(T⁷I,S⁶F),
(T¹¹I,S¹⁰F),
(T²Q,S²R),
(T⁶Q,S⁶R),
(T¹⁰Q,S¹⁰R),
(TIQ,S⁸RF),
(T⁵IQ,RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S²F),
(T⁷I,S⁶F),
(T¹¹I,S¹⁰F),
(T²Q,S⁸R),
(T⁶Q,R),
(T¹⁰Q,S⁴R),
(TIQ,S²RF),
(T⁵IQ,S⁶RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S⁶F),
(T⁷I,S¹⁰F),
(T¹¹I,S²F),
(T²Q,R),
(T⁶Q,S⁴R),
(T¹⁰Q,S⁸R),
(TIQ,S²RF),
(T⁵IQ,S⁶RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S⁶F),
(T⁷I,S¹⁰F),
(T¹¹I,S²F),
(T²Q,S⁶R),
(T⁶Q,S¹⁰R),
(T¹⁰Q,S²R),
(TIQ,S⁸RF),
(T⁵IQ,RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S¹⁰F),
(T⁷I,S²F),
(T¹¹I,S⁶F),
(T²Q,S⁴R),
(T⁶Q,S⁸R),
(T¹⁰Q,R),
(TIQ,S²RF),
(T⁵IQ,S⁶RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T³I,S¹⁰F),
(T⁷I,S²F),
(T¹¹I,S⁶F),
(T²Q,S¹⁰R),
(T⁶Q,S²R),
(T¹⁰Q,S⁶R),
(TIQ,S⁸RF),
(T⁵IQ,RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S²F),
(T⁵I,S¹⁰F),
(T⁹I,S⁶F),
(T²Q,S²R),
(T⁶Q,S¹⁰R),
(T¹⁰Q,S⁶R),
(T³IQ,S⁴RF),
(T⁷IQ,RF),
(T¹¹IQ,S⁸RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S²F),
(T⁵I,S¹⁰F),
(T⁹I,S⁶F),
(T²Q,S⁸R),
(T⁶Q,S⁴R),
(T¹⁰Q,R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S⁶RF),
(T¹¹IQ,S²RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S⁶F),
(T⁵I,S²F),
(T⁹I,S¹⁰F),
(T²Q,R),
(T⁶Q,S⁸R),
(T¹⁰Q,S⁴R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S⁶RF),
(T¹¹IQ,S²RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S⁶F),
(T⁵I,S²F),
(T⁹I,S¹⁰F),
(T²Q,S⁶R),
(T⁶Q,S²R),
(T¹⁰Q,S¹⁰R),
(T³IQ,S⁴RF),
(T⁷IQ,RF),
(T¹¹IQ,S⁸RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S¹⁰F),
(T⁵I,S⁶F),
(T⁹I,S²F),
(T²Q,S⁴R),
(T⁶Q,R),
(T¹⁰Q,S⁸R),
(T³IQ,S¹⁰RF),
(T⁷IQ,S⁶RF),
(T¹¹IQ,S²RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(TI,S¹⁰F),
(T⁵I,S⁶F),
(T⁹I,S²F),
(T²Q,S¹⁰R),
(T⁶Q,S⁶R),
(T¹⁰Q,S²R),
(T³IQ,S⁴RF),
(T⁷IQ,RF),
(T¹¹IQ,S⁸RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S²F),
(T⁷I,S¹⁰F),
(T¹¹I,S⁶F),
(T²Q,S⁴R),
(T⁶Q,R),
(T¹⁰Q,S⁸R),
(TIQ,S⁶RF),
(T⁵IQ,S²RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S²F),
(T⁷I,S¹⁰F),
(T¹¹I,S⁶F),
(T²Q,S¹⁰R),
(T⁶Q,S⁶R),
(T¹⁰Q,S²R),
(TIQ,RF),
(T⁵IQ,S⁸RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S⁶F),
(T⁷I,S²F),
(T¹¹I,S¹⁰F),
(T²Q,S²R),
(T⁶Q,S¹⁰R),
(T¹⁰Q,S⁶R),
(TIQ,RF),
(T⁵IQ,S⁸RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S⁶F),
(T⁷I,S²F),
(T¹¹I,S¹⁰F),
(T²Q,S⁸R),
(T⁶Q,S⁴R),
(T¹⁰Q,R),
(TIQ,S⁶RF),
(T⁵IQ,S²RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S¹⁰F),
(T⁷I,S⁶F),
(T¹¹I,S²F),
(T²Q,R),
(T⁶Q,S⁸R),
(T¹⁰Q,S⁴R),
(TIQ,S⁶RF),
(T⁵IQ,S²RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T³I,S¹⁰F),
(T⁷I,S⁶F),
(T¹¹I,S²F),
(T²Q,S⁶R),
(T⁶Q,S²R),
(T¹⁰Q,S¹⁰R),
(TIQ,RF),
(T⁵IQ,S⁸RF),
(T⁹IQ,S⁴RF).

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 X83

Stabilizer type X₈₃