Stabilizer type X₇₀

Acting group: Aff₁(Z₁₂) × Aff₁(Z₁₂)
There are exactly 12 groups in this conjugacy class.
The group order is 8.

(T⁰,S⁰),
(T⁶,S⁶),
(TI,S⁴RF),
(T⁷I,S¹⁰RF),
(TQ,S³),
(T⁷Q,S⁹),
(IQ,SRF),
(T⁶IQ,S⁷RF).

(T⁰,S⁰),
(T⁶,S⁶),
(TI,S⁴RF),
(T⁷I,S¹⁰RF),
(TQ,S⁹),
(T⁷Q,S³),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(TI,S¹⁰RF),
(T⁷I,S⁴RF),
(TQ,S³),
(T⁷Q,S⁹),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(TI,S¹⁰RF),
(T⁷I,S⁴RF),
(TQ,S⁹),
(T⁷Q,S³),
(IQ,SRF),
(T⁶IQ,S⁷RF).

(T⁰,S⁰),
(T⁶,S⁶),
(T³I,S⁴RF),
(T⁹I,S¹⁰RF),
(T³Q,S³),
(T⁹Q,S⁹),
(IQ,SRF),
(T⁶IQ,S⁷RF).

(T⁰,S⁰),
(T⁶,S⁶),
(T³I,S⁴RF),
(T⁹I,S¹⁰RF),
(T³Q,S⁹),
(T⁹Q,S³),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(T³I,S¹⁰RF),
(T⁹I,S⁴RF),
(T³Q,S³),
(T⁹Q,S⁹),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(T³I,S¹⁰RF),
(T⁹I,S⁴RF),
(T³Q,S⁹),
(T⁹Q,S³),
(IQ,SRF),
(T⁶IQ,S⁷RF).

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵I,S⁴RF),
(T¹¹I,S¹⁰RF),
(T⁵Q,S³),
(T¹¹Q,S⁹),
(IQ,SRF),
(T⁶IQ,S⁷RF).

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵I,S⁴RF),
(T¹¹I,S¹⁰RF),
(T⁵Q,S⁹),
(T¹¹Q,S³),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵I,S¹⁰RF),
(T¹¹I,S⁴RF),
(T⁵Q,S³),
(T¹¹Q,S⁹),
(IQ,S⁷RF),
(T⁶IQ,SRF).

(T⁰,S⁰),
(T⁶,S⁶),
(T⁵I,S¹⁰RF),
(T¹¹I,S⁴RF),
(T⁵Q,S⁹),
(T¹¹Q,S³),
(IQ,SRF),
(T⁶IQ,S⁷RF).

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 X70

Stabilizer type X₇₀