Stabilizer type X12
Acting group: Aff1(Z12) × Aff1(Z12)
There are exactly 18 groups in this conjugacy class.
The group order is 2.
(T0,S0),
(TI,S2F).
(T0,S0),
(TI,S6F).
(T0,S0),
(TI,S10F).
(T0,S0),
(T3I,S2F).
(T0,S0),
(T3I,S6F).
(T0,S0),
(T3I,S10F).
(T0,S0),
(T5I,S2F).
(T0,S0),
(T5I,S6F).
(T0,S0),
(T5I,S10F).
(T0,S0),
(T7I,S2F).
(T0,S0),
(T7I,S6F).
(T0,S0),
(T7I,S10F).
(T0,S0),
(T9I,S2F).
(T0,S0),
(T9I,S6F).
(T0,S0),
(T9I,S10F).
(T0,S0),
(T11I,S2F).
(T0,S0),
(T11I,S6F).
(T0,S0),
(T11I,S10F).
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)
.
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