Stabilizer type X₈₁

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),
(I,SR),
(T⁴I,S⁵R),
(T⁸I,S⁹R),
(T²Q,S²F),
(T⁶Q,S⁶F),
(T¹⁰Q,S¹⁰F),
(T²IQ,S³RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(I,S³R),
(T⁴I,S⁷R),
(T⁸I,S¹¹R),
(T²Q,S¹⁰F),
(T⁶Q,S²F),
(T¹⁰Q,S⁶F),
(T²IQ,S⁹RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁵RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(I,S⁵R),
(T⁴I,S⁹R),
(T⁸I,SR),
(T²Q,S⁶F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S²F),
(T²IQ,S³RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(I,S⁷R),
(T⁴I,S¹¹R),
(T⁸I,S³R),
(T²Q,S²F),
(T⁶Q,S⁶F),
(T¹⁰Q,S¹⁰F),
(T²IQ,S⁹RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁵RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(I,S⁹R),
(T⁴I,SR),
(T⁸I,S⁵R),
(T²Q,S¹⁰F),
(T⁶Q,S²F),
(T¹⁰Q,S⁶F),
(T²IQ,S³RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(I,S¹¹R),
(T⁴I,S³R),
(T⁸I,S⁷R),
(T²Q,S⁶F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S²F),
(T²IQ,S⁹RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁵RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,SR),
(T⁶I,S⁵R),
(T¹⁰I,S⁹R),
(T²Q,S⁶F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S²F),
(IQ,S⁷RF),
(T⁴IQ,S¹¹RF),
(T⁸IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,S³R),
(T⁶I,S⁷R),
(T¹⁰I,S¹¹R),
(T²Q,S²F),
(T⁶Q,S⁶F),
(T¹⁰Q,S¹⁰F),
(IQ,SRF),
(T⁴IQ,S⁵RF),
(T⁸IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,S⁵R),
(T⁶I,S⁹R),
(T¹⁰I,SR),
(T²Q,S¹⁰F),
(T⁶Q,S²F),
(T¹⁰Q,S⁶F),
(IQ,S⁷RF),
(T⁴IQ,S¹¹RF),
(T⁸IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,S⁷R),
(T⁶I,S¹¹R),
(T¹⁰I,S³R),
(T²Q,S⁶F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S²F),
(IQ,SRF),
(T⁴IQ,S⁵RF),
(T⁸IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,S⁹R),
(T⁶I,SR),
(T¹⁰I,S⁵R),
(T²Q,S²F),
(T⁶Q,S⁶F),
(T¹⁰Q,S¹⁰F),
(IQ,S⁷RF),
(T⁴IQ,S¹¹RF),
(T⁸IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁴),
(T⁸,S⁸),
(T²I,S¹¹R),
(T⁶I,S³R),
(T¹⁰I,S⁷R),
(T²Q,S¹⁰F),
(T⁶Q,S²F),
(T¹⁰Q,S⁶F),
(IQ,SRF),
(T⁴IQ,S⁵RF),
(T⁸IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,SR),
(T⁴I,S⁹R),
(T⁸I,S⁵R),
(T²Q,S¹⁰F),
(T⁶Q,S⁶F),
(T¹⁰Q,S²F),
(T²IQ,S¹¹RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,S³R),
(T⁴I,S¹¹R),
(T⁸I,S⁷R),
(T²Q,S⁶F),
(T⁶Q,S²F),
(T¹⁰Q,S¹⁰F),
(T²IQ,S⁵RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,S⁵R),
(T⁴I,SR),
(T⁸I,S⁹R),
(T²Q,S²F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S⁶F),
(T²IQ,S¹¹RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,S⁷R),
(T⁴I,S³R),
(T⁸I,S¹¹R),
(T²Q,S¹⁰F),
(T⁶Q,S⁶F),
(T¹⁰Q,S²F),
(T²IQ,S⁵RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,S⁹R),
(T⁴I,S⁵R),
(T⁸I,SR),
(T²Q,S⁶F),
(T⁶Q,S²F),
(T¹⁰Q,S¹⁰F),
(T²IQ,S¹¹RF),
(T⁶IQ,S⁷RF),
(T¹⁰IQ,S³RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(I,S¹¹R),
(T⁴I,S⁷R),
(T⁸I,S³R),
(T²Q,S²F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S⁶F),
(T²IQ,S⁵RF),
(T⁶IQ,SRF),
(T¹⁰IQ,S⁹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,SR),
(T⁶I,S⁹R),
(T¹⁰I,S⁵R),
(T²Q,S⁶F),
(T⁶Q,S²F),
(T¹⁰Q,S¹⁰F),
(IQ,S⁷RF),
(T⁴IQ,S³RF),
(T⁸IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,S³R),
(T⁶I,S¹¹R),
(T¹⁰I,S⁷R),
(T²Q,S²F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S⁶F),
(IQ,SRF),
(T⁴IQ,S⁹RF),
(T⁸IQ,S⁵RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,S⁵R),
(T⁶I,SR),
(T¹⁰I,S⁹R),
(T²Q,S¹⁰F),
(T⁶Q,S⁶F),
(T¹⁰Q,S²F),
(IQ,S⁷RF),
(T⁴IQ,S³RF),
(T⁸IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,S⁷R),
(T⁶I,S³R),
(T¹⁰I,S¹¹R),
(T²Q,S⁶F),
(T⁶Q,S²F),
(T¹⁰Q,S¹⁰F),
(IQ,SRF),
(T⁴IQ,S⁹RF),
(T⁸IQ,S⁵RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,S⁹R),
(T⁶I,S⁵R),
(T¹⁰I,SR),
(T²Q,S²F),
(T⁶Q,S¹⁰F),
(T¹⁰Q,S⁶F),
(IQ,S⁷RF),
(T⁴IQ,S³RF),
(T⁸IQ,S¹¹RF).

(T⁰,S⁰),
(T⁴,S⁸),
(T⁸,S⁴),
(T²I,S¹¹R),
(T⁶I,S⁷R),
(T¹⁰I,S³R),
(T²Q,S¹⁰F),
(T⁶Q,S⁶F),
(T¹⁰Q,S²F),
(IQ,SRF),
(T⁴IQ,S⁹RF),
(T⁸IQ,S⁵RF).

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 X81

Stabilizer type X₈₁