Stabilizer type Y₅₅

Acting group: 𝔄₁₂
There are exactly 36 groups in this conjugacy class.
The group order is 8.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,SF),
(T⁷Q,S⁷F),
(TI,S²R) ∘ P,
(T⁷I,S⁸R) ∘ P,
(IQ,SRF) ∘ P,
(T⁶IQ,S⁷RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,SF),
(T⁷Q,S⁷F),
(T⁴I,S⁵R) ∘ P,
(T¹⁰I,S¹¹R) ∘ P,
(T³IQ,S⁴RF) ∘ P,
(T⁹IQ,S¹⁰RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S³F),
(T⁷Q,S⁹F),
(T²,S¹⁰) ∘ P,
(T⁸,S⁴) ∘ P,
(T⁵Q,S¹¹F) ∘ P,
(T¹¹Q,S⁵F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S³F),
(T⁷Q,S⁹F),
(T⁵,S⁷) ∘ P,
(T¹¹,S) ∘ P,
(T²Q,S²F) ∘ P,
(T⁸Q,S⁸F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁵F),
(T⁷Q,S¹¹F),
(I,SR) ∘ P,
(T⁶I,S⁷R) ∘ P,
(TIQ,S⁶RF) ∘ P,
(T⁷IQ,RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁵F),
(T⁷Q,S¹¹F),
(T³I,S⁴R) ∘ P,
(T⁹I,S¹⁰R) ∘ P,
(T⁴IQ,S⁹RF) ∘ P,
(T¹⁰IQ,S³RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁷F),
(T⁷Q,SF),
(T⁰,S⁰) ∘ P,
(T⁶,S⁶) ∘ P,
(TQ,S⁷F) ∘ P,
(T⁷Q,SF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁷F),
(T⁷Q,SF),
(T³,S⁹) ∘ P,
(T⁹,S³) ∘ P,
(T⁴Q,S⁴F) ∘ P,
(T¹⁰Q,S¹⁰F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁹F),
(T⁷Q,S³F),
(T²I,S³R) ∘ P,
(T⁸I,S⁹R) ∘ P,
(T⁵IQ,S²RF) ∘ P,
(T¹¹IQ,S⁸RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S⁹F),
(T⁷Q,S³F),
(T⁵I,S⁶R) ∘ P,
(T¹¹I,R) ∘ P,
(T²IQ,S¹¹RF) ∘ P,
(T⁸IQ,S⁵RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S¹¹F),
(T⁷Q,S⁵F),
(T,S¹¹) ∘ P,
(T⁷,S⁵) ∘ P,
(Q,F) ∘ P,
(T⁶Q,S⁶F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(TQ,S¹¹F),
(T⁷Q,S⁵F),
(T⁴,S⁸) ∘ P,
(T¹⁰,S²) ∘ P,
(T³Q,S⁹F) ∘ P,
(T⁹Q,S³F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,SF),
(T⁹Q,S⁷F),
(T,S¹¹) ∘ P,
(T⁷,S⁵) ∘ P,
(T²Q,S²F) ∘ P,
(T⁸Q,S⁸F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,SF),
(T⁹Q,S⁷F),
(T⁴,S⁸) ∘ P,
(T¹⁰,S²) ∘ P,
(T⁵Q,S¹¹F) ∘ P,
(T¹¹Q,S⁵F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S³F),
(T⁹Q,S⁹F),
(I,SR) ∘ P,
(T⁶I,S⁷R) ∘ P,
(T³IQ,S⁴RF) ∘ P,
(T⁹IQ,S¹⁰RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S³F),
(T⁹Q,S⁹F),
(T³I,S⁴R) ∘ P,
(T⁹I,S¹⁰R) ∘ P,
(IQ,SRF) ∘ P,
(T⁶IQ,S⁷RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁵F),
(T⁹Q,S¹¹F),
(T²,S¹⁰) ∘ P,
(T⁸,S⁴) ∘ P,
(TQ,S⁷F) ∘ P,
(T⁷Q,SF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁵F),
(T⁹Q,S¹¹F),
(T⁵,S⁷) ∘ P,
(T¹¹,S) ∘ P,
(T⁴Q,S⁴F) ∘ P,
(T¹⁰Q,S¹⁰F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁷F),
(T⁹Q,SF),
(T²I,S³R) ∘ P,
(T⁸I,S⁹R) ∘ P,
(TIQ,S⁶RF) ∘ P,
(T⁷IQ,RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁷F),
(T⁹Q,SF),
(T⁵I,S⁶R) ∘ P,
(T¹¹I,R) ∘ P,
(T⁴IQ,S⁹RF) ∘ P,
(T¹⁰IQ,S³RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁹F),
(T⁹Q,S³F),
(T⁰,S⁰) ∘ P,
(T⁶,S⁶) ∘ P,
(T³Q,S⁹F) ∘ P,
(T⁹Q,S³F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S⁹F),
(T⁹Q,S³F),
(T³,S⁹) ∘ P,
(T⁹,S³) ∘ P,
(Q,F) ∘ P,
(T⁶Q,S⁶F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S¹¹F),
(T⁹Q,S⁵F),
(TI,S²R) ∘ P,
(T⁷I,S⁸R) ∘ P,
(T²IQ,S¹¹RF) ∘ P,
(T⁸IQ,S⁵RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T³Q,S¹¹F),
(T⁹Q,S⁵F),
(T⁴I,S⁵R) ∘ P,
(T¹⁰I,S¹¹R) ∘ P,
(T⁵IQ,S²RF) ∘ P,
(T¹¹IQ,S⁸RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,SF),
(T¹¹Q,S⁷F),
(I,SR) ∘ P,
(T⁶I,S⁷R) ∘ P,
(T⁵IQ,S²RF) ∘ P,
(T¹¹IQ,S⁸RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,SF),
(T¹¹Q,S⁷F),
(T³I,S⁴R) ∘ P,
(T⁹I,S¹⁰R) ∘ P,
(T²IQ,S¹¹RF) ∘ P,
(T⁸IQ,S⁵RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S³F),
(T¹¹Q,S⁹F),
(T,S¹¹) ∘ P,
(T⁷,S⁵) ∘ P,
(T⁴Q,S⁴F) ∘ P,
(T¹⁰Q,S¹⁰F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S³F),
(T¹¹Q,S⁹F),
(T⁴,S⁸) ∘ P,
(T¹⁰,S²) ∘ P,
(TQ,S⁷F) ∘ P,
(T⁷Q,SF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁵F),
(T¹¹Q,S¹¹F),
(T²I,S³R) ∘ P,
(T⁸I,S⁹R) ∘ P,
(T³IQ,S⁴RF) ∘ P,
(T⁹IQ,S¹⁰RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁵F),
(T¹¹Q,S¹¹F),
(T⁵I,S⁶R) ∘ P,
(T¹¹I,R) ∘ P,
(IQ,SRF) ∘ P,
(T⁶IQ,S⁷RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁷F),
(T¹¹Q,SF),
(T²,S¹⁰) ∘ P,
(T⁸,S⁴) ∘ P,
(T³Q,S⁹F) ∘ P,
(T⁹Q,S³F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁷F),
(T¹¹Q,SF),
(T⁵,S⁷) ∘ P,
(T¹¹,S) ∘ P,
(Q,F) ∘ P,
(T⁶Q,S⁶F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁹F),
(T¹¹Q,S³F),
(TI,S²R) ∘ P,
(T⁷I,S⁸R) ∘ P,
(T⁴IQ,S⁹RF) ∘ P,
(T¹⁰IQ,S³RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S⁹F),
(T¹¹Q,S³F),
(T⁴I,S⁵R) ∘ P,
(T¹⁰I,S¹¹R) ∘ P,
(TIQ,S⁶RF) ∘ P,
(T⁷IQ,RF) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S¹¹F),
(T¹¹Q,S⁵F),
(T⁰,S⁰) ∘ P,
(T⁶,S⁶) ∘ P,
(T⁵Q,S¹¹F) ∘ P,
(T¹¹Q,S⁵F) ∘ P.

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵Q,S¹¹F),
(T¹¹Q,S⁵F),
(T³,S⁹) ∘ P,
(T⁹,S³) ∘ P,
(T²Q,S²F) ∘ P,
(T⁸Q,S⁸F) ∘ P.

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 Y55

Stabilizer type Y₅₅