Stabilizer type X₈₇

Acting group: Aff₁(Z₁₂) × Aff₁(Z₁₂)
There are exactly 36 groups in this conjugacy class.
The group order is 16.

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,SR),
(T³I,S⁴R),
(T⁶I,S⁷R),
(T⁹I,S¹⁰R),
(Q,F),
(T³Q,S³F),
(T⁶Q,S⁶F),
(T⁹Q,S⁹F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,S³R),
(T³I,S⁶R),
(T⁶I,S⁹R),
(T⁹I,R),
(Q,S⁸F),
(T³Q,S¹¹F),
(T⁶Q,S²F),
(T⁹Q,S⁵F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,S⁵R),
(T³I,S⁸R),
(T⁶I,S¹¹R),
(T⁹I,S²R),
(Q,S⁴F),
(T³Q,S⁷F),
(T⁶Q,S¹⁰F),
(T⁹Q,SF),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,S⁷R),
(T³I,S¹⁰R),
(T⁶I,SR),
(T⁹I,S⁴R),
(Q,F),
(T³Q,S³F),
(T⁶Q,S⁶F),
(T⁹Q,S⁹F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,S⁹R),
(T³I,R),
(T⁶I,S³R),
(T⁹I,S⁶R),
(Q,S⁸F),
(T³Q,S¹¹F),
(T⁶Q,S²F),
(T⁹Q,S⁵F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(I,S¹¹R),
(T³I,S²R),
(T⁶I,S⁵R),
(T⁹I,S⁸R),
(Q,S⁴F),
(T³Q,S⁷F),
(T⁶Q,S¹⁰F),
(T⁹Q,SF),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,R),
(T⁴I,S³R),
(T⁷I,S⁶R),
(T¹⁰I,S⁹R),
(TQ,S⁵F),
(T⁴Q,S⁸F),
(T⁷Q,S¹¹F),
(T¹⁰Q,S²F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,S²R),
(T⁴I,S⁵R),
(T⁷I,S⁸R),
(T¹⁰I,S¹¹R),
(TQ,SF),
(T⁴Q,S⁴F),
(T⁷Q,S⁷F),
(T¹⁰Q,S¹⁰F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,S⁴R),
(T⁴I,S⁷R),
(T⁷I,S¹⁰R),
(T¹⁰I,SR),
(TQ,S⁹F),
(T⁴Q,F),
(T⁷Q,S³F),
(T¹⁰Q,S⁶F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,S⁶R),
(T⁴I,S⁹R),
(T⁷I,R),
(T¹⁰I,S³R),
(TQ,S⁵F),
(T⁴Q,S⁸F),
(T⁷Q,S¹¹F),
(T¹⁰Q,S²F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,S⁸R),
(T⁴I,S¹¹R),
(T⁷I,S²R),
(T¹⁰I,S⁵R),
(TQ,SF),
(T⁴Q,S⁴F),
(T⁷Q,S⁷F),
(T¹⁰Q,S¹⁰F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(TI,S¹⁰R),
(T⁴I,SR),
(T⁷I,S⁴R),
(T¹⁰I,S⁷R),
(TQ,S⁹F),
(T⁴Q,F),
(T⁷Q,S³F),
(T¹⁰Q,S⁶F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,SR),
(T⁵I,S⁴R),
(T⁸I,S⁷R),
(T¹¹I,S¹⁰R),
(T²Q,S⁶F),
(T⁵Q,S⁹F),
(T⁸Q,F),
(T¹¹Q,S³F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,S³R),
(T⁵I,S⁶R),
(T⁸I,S⁹R),
(T¹¹I,R),
(T²Q,S²F),
(T⁵Q,S⁵F),
(T⁸Q,S⁸F),
(T¹¹Q,S¹¹F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,S⁵R),
(T⁵I,S⁸R),
(T⁸I,S¹¹R),
(T¹¹I,S²R),
(T²Q,S¹⁰F),
(T⁵Q,SF),
(T⁸Q,S⁴F),
(T¹¹Q,S⁷F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,S⁷R),
(T⁵I,S¹⁰R),
(T⁸I,SR),
(T¹¹I,S⁴R),
(T²Q,S⁶F),
(T⁵Q,S⁹F),
(T⁸Q,F),
(T¹¹Q,S³F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,S⁹R),
(T⁵I,R),
(T⁸I,S³R),
(T¹¹I,S⁶R),
(T²Q,S²F),
(T⁵Q,S⁵F),
(T⁸Q,S⁸F),
(T¹¹Q,S¹¹F),
(IQ,S⁷RF),
(T³IQ,S¹⁰RF),
(T⁶IQ,SRF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S³),
(T⁶,S⁶),
(T⁹,S⁹),
(T²I,S¹¹R),
(T⁵I,S²R),
(T⁸I,S⁵R),
(T¹¹I,S⁸R),
(T²Q,S¹⁰F),
(T⁵Q,SF),
(T⁸Q,S⁴F),
(T¹¹Q,S⁷F),
(IQ,SRF),
(T³IQ,S⁴RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,SR),
(T³I,S¹⁰R),
(T⁶I,S⁷R),
(T⁹I,S⁴R),
(Q,F),
(T³Q,S⁹F),
(T⁶Q,S⁶F),
(T⁹Q,S³F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,S³R),
(T³I,R),
(T⁶I,S⁹R),
(T⁹I,S⁶R),
(Q,S⁸F),
(T³Q,S⁵F),
(T⁶Q,S²F),
(T⁹Q,S¹¹F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,S⁵R),
(T³I,S²R),
(T⁶I,S¹¹R),
(T⁹I,S⁸R),
(Q,S⁴F),
(T³Q,SF),
(T⁶Q,S¹⁰F),
(T⁹Q,S⁷F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,S⁷R),
(T³I,S⁴R),
(T⁶I,SR),
(T⁹I,S¹⁰R),
(Q,F),
(T³Q,S⁹F),
(T⁶Q,S⁶F),
(T⁹Q,S³F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,S⁹R),
(T³I,S⁶R),
(T⁶I,S³R),
(T⁹I,R),
(Q,S⁸F),
(T³Q,S⁵F),
(T⁶Q,S²F),
(T⁹Q,S¹¹F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(I,S¹¹R),
(T³I,S⁸R),
(T⁶I,S⁵R),
(T⁹I,S²R),
(Q,S⁴F),
(T³Q,SF),
(T⁶Q,S¹⁰F),
(T⁹Q,S⁷F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,R),
(T⁴I,S⁹R),
(T⁷I,S⁶R),
(T¹⁰I,S³R),
(TQ,S¹¹F),
(T⁴Q,S⁸F),
(T⁷Q,S⁵F),
(T¹⁰Q,S²F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,S²R),
(T⁴I,S¹¹R),
(T⁷I,S⁸R),
(T¹⁰I,S⁵R),
(TQ,S⁷F),
(T⁴Q,S⁴F),
(T⁷Q,SF),
(T¹⁰Q,S¹⁰F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,S⁴R),
(T⁴I,SR),
(T⁷I,S¹⁰R),
(T¹⁰I,S⁷R),
(TQ,S³F),
(T⁴Q,F),
(T⁷Q,S⁹F),
(T¹⁰Q,S⁶F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,S⁶R),
(T⁴I,S³R),
(T⁷I,R),
(T¹⁰I,S⁹R),
(TQ,S¹¹F),
(T⁴Q,S⁸F),
(T⁷Q,S⁵F),
(T¹⁰Q,S²F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,S⁸R),
(T⁴I,S⁵R),
(T⁷I,S²R),
(T¹⁰I,S¹¹R),
(TQ,S⁷F),
(T⁴Q,S⁴F),
(T⁷Q,SF),
(T¹⁰Q,S¹⁰F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(TI,S¹⁰R),
(T⁴I,S⁷R),
(T⁷I,S⁴R),
(T¹⁰I,SR),
(TQ,S³F),
(T⁴Q,F),
(T⁷Q,S⁹F),
(T¹⁰Q,S⁶F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,SR),
(T⁵I,S¹⁰R),
(T⁸I,S⁷R),
(T¹¹I,S⁴R),
(T²Q,S⁶F),
(T⁵Q,S³F),
(T⁸Q,F),
(T¹¹Q,S⁹F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,S³R),
(T⁵I,R),
(T⁸I,S⁹R),
(T¹¹I,S⁶R),
(T²Q,S²F),
(T⁵Q,S¹¹F),
(T⁸Q,S⁸F),
(T¹¹Q,S⁵F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,S⁵R),
(T⁵I,S²R),
(T⁸I,S¹¹R),
(T¹¹I,S⁸R),
(T²Q,S¹⁰F),
(T⁵Q,S⁷F),
(T⁸Q,S⁴F),
(T¹¹Q,SF),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,S⁷R),
(T⁵I,S⁴R),
(T⁸I,SR),
(T¹¹I,S¹⁰R),
(T²Q,S⁶F),
(T⁵Q,S³F),
(T⁸Q,F),
(T¹¹Q,S⁹F),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(T⁹IQ,S⁴RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,S⁹R),
(T⁵I,S⁶R),
(T⁸I,S³R),
(T¹¹I,R),
(T²Q,S²F),
(T⁵Q,S¹¹F),
(T⁸Q,S⁸F),
(T¹¹Q,S⁵F),
(IQ,S⁷RF),
(T³IQ,S⁴RF),
(T⁶IQ,SRF),
(T⁹IQ,S¹⁰RF).

(T⁰,S⁰),
(T³,S⁹),
(T⁶,S⁶),
(T⁹,S³),
(T²I,S¹¹R),
(T⁵I,S⁸R),
(T⁸I,S⁵R),
(T¹¹I,S²R),
(T²Q,S¹⁰F),
(T⁵Q,S⁷F),
(T⁸Q,S⁴F),
(T¹¹Q,SF),
(IQ,SRF),
(T³IQ,S¹⁰RF),
(T⁶IQ,S⁷RF),
(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 X87

Stabilizer type X₈₇