Stabilizer type X61

Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 8 groups in this conjugacy class.
The group order is 6.
(T0,S0),
(T4,S4),
(T8,S8),
(IQ,SRF),
(T4IQ,S5RF),
(T8IQ,S9RF).
(T0,S0),
(T4,S4),
(T8,S8),
(IQ,S7RF),
(T4IQ,S11RF),
(T8IQ,S3RF).
(T0,S0),
(T4,S4),
(T8,S8),
(T2IQ,S3RF),
(T6IQ,S7RF),
(T10IQ,S11RF).
(T0,S0),
(T4,S4),
(T8,S8),
(T2IQ,S9RF),
(T6IQ,SRF),
(T10IQ,S5RF).
(T0,S0),
(T4,S8),
(T8,S4),
(IQ,SRF),
(T4IQ,S9RF),
(T8IQ,S5RF).
(T0,S0),
(T4,S8),
(T8,S4),
(IQ,S7RF),
(T4IQ,S3RF),
(T8IQ,S11RF).
(T0,S0),
(T4,S8),
(T8,S4),
(T2IQ,S5RF),
(T6IQ,SRF),
(T10IQ,S9RF).
(T0,S0),
(T4,S8),
(T8,S4),
(T2IQ,S11RF),
(T6IQ,S7RF),
(T10IQ,S3RF).

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