Stabilizer type Y60

Acting group: 𝔄12
There are exactly 48 groups in this conjugacy class.
The group order is 8.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T0,S0) ∘ P,
(T6,S4RF) ∘ P,
(T3IQ,S6) ∘ P,
(T9IQ,S10RF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T0,S10RF) ∘ P,
(T6,S6) ∘ P,
(T3IQ,S4RF) ∘ P,
(T9IQ,S0) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(TI,S2R) ∘ P,
(T7I,S10F) ∘ P,
(T4Q,S4F) ∘ P,
(T10Q,S8R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(TI,S4F) ∘ P,
(T7I,S8R) ∘ P,
(T4Q,S2R) ∘ P,
(T10Q,S10F) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T2,S8RF) ∘ P,
(T8,S4) ∘ P,
(T5IQ,S2RF) ∘ P,
(T11IQ,S10) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T2,S10) ∘ P,
(T8,S2RF) ∘ P,
(T5IQ,S4) ∘ P,
(T11IQ,S8RF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T3I,S4R) ∘ P,
(T9I,F) ∘ P,
(Q,S10R) ∘ P,
(T6Q,S6F) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T3I,S6F) ∘ P,
(T9I,S10R) ∘ P,
(Q,F) ∘ P,
(T6Q,S4R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T4,S6RF) ∘ P,
(T10,S2) ∘ P,
(TIQ,S8) ∘ P,
(T7IQ,RF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T4,S8) ∘ P,
(T10,RF) ∘ P,
(TIQ,S6RF) ∘ P,
(T7IQ,S2) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T5I,S6R) ∘ P,
(T11I,S2F) ∘ P,
(T2Q,R) ∘ P,
(T8Q,S8F) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S6),
(T9IQ,S10RF),
(T5I,S8F) ∘ P,
(T11I,R) ∘ P,
(T2Q,S2F) ∘ P,
(T8Q,S6R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(I,SR) ∘ P,
(T6I,S3F) ∘ P,
(T3Q,S9F) ∘ P,
(T9Q,S7R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(I,S9F) ∘ P,
(T6I,S7R) ∘ P,
(T3Q,SR) ∘ P,
(T9Q,S3F) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T,S3RF) ∘ P,
(T7,S5) ∘ P,
(T4IQ,S9RF) ∘ P,
(T10IQ,S11) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T,S11) ∘ P,
(T7,S9RF) ∘ P,
(T4IQ,S5) ∘ P,
(T10IQ,S3RF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T2I,S3R) ∘ P,
(T8I,S5F) ∘ P,
(T5Q,S11F) ∘ P,
(T11Q,S9R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T2I,S11F) ∘ P,
(T8I,S9R) ∘ P,
(T5Q,S3R) ∘ P,
(T11Q,S5F) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T3,SRF) ∘ P,
(T9,S3) ∘ P,
(IQ,S9) ∘ P,
(T6IQ,S7RF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T3,S9) ∘ P,
(T9,S7RF) ∘ P,
(IQ,SRF) ∘ P,
(T6IQ,S3) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T4I,SF) ∘ P,
(T10I,S11R) ∘ P,
(TQ,S7F) ∘ P,
(T7Q,S5R) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T4I,S5R) ∘ P,
(T10I,S7F) ∘ P,
(TQ,S11R) ∘ P,
(T7Q,SF) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T5,S7) ∘ P,
(T11,S5RF) ∘ P,
(T2IQ,S11RF) ∘ P,
(T8IQ,S) ∘ P.
(T0,S0),
(T6,S4RF),
(T3IQ,S10RF),
(T9IQ,S6),
(T5,S11RF) ∘ P,
(T11,S) ∘ P,
(T2IQ,S7) ∘ P,
(T8IQ,S5RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T0,S0) ∘ P,
(T6,S10RF) ∘ P,
(T3IQ,S4RF) ∘ P,
(T9IQ,S6) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T0,S4RF) ∘ P,
(T6,S6) ∘ P,
(T3IQ,S0) ∘ P,
(T9IQ,S10RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(TI,S2R) ∘ P,
(T7I,S4F) ∘ P,
(T4Q,S8R) ∘ P,
(T10Q,S10F) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(TI,S10F) ∘ P,
(T7I,S8R) ∘ P,
(T4Q,S4F) ∘ P,
(T10Q,S2R) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T2,S2RF) ∘ P,
(T8,S4) ∘ P,
(T5IQ,S10) ∘ P,
(T11IQ,S8RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T2,S10) ∘ P,
(T8,S8RF) ∘ P,
(T5IQ,S2RF) ∘ P,
(T11IQ,S4) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T3I,F) ∘ P,
(T9I,S10R) ∘ P,
(Q,S4R) ∘ P,
(T6Q,S6F) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T3I,S4R) ∘ P,
(T9I,S6F) ∘ P,
(Q,F) ∘ P,
(T6Q,S10R) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T4,RF) ∘ P,
(T10,S2) ∘ P,
(TIQ,S6RF) ∘ P,
(T7IQ,S8) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T4,S8) ∘ P,
(T10,S6RF) ∘ P,
(TIQ,S2) ∘ P,
(T7IQ,RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T5I,S2F) ∘ P,
(T11I,R) ∘ P,
(T2Q,S6R) ∘ P,
(T8Q,S8F) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S4RF),
(T9IQ,S6),
(T5I,S6R) ∘ P,
(T11I,S8F) ∘ P,
(T2Q,S2F) ∘ P,
(T8Q,R) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(I,SR) ∘ P,
(T6I,S9F) ∘ P,
(T3Q,S7R) ∘ P,
(T9Q,S3F) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(I,S3F) ∘ P,
(T6I,S7R) ∘ P,
(T3Q,S9F) ∘ P,
(T9Q,SR) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T,S9RF) ∘ P,
(T7,S5) ∘ P,
(T4IQ,S11) ∘ P,
(T10IQ,S3RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T,S11) ∘ P,
(T7,S3RF) ∘ P,
(T4IQ,S9RF) ∘ P,
(T10IQ,S5) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T2I,S3R) ∘ P,
(T8I,S11F) ∘ P,
(T5Q,S9R) ∘ P,
(T11Q,S5F) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T2I,S5F) ∘ P,
(T8I,S9R) ∘ P,
(T5Q,S11F) ∘ P,
(T11Q,S3R) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T3,S7RF) ∘ P,
(T9,S3) ∘ P,
(IQ,SRF) ∘ P,
(T6IQ,S9) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T3,S9) ∘ P,
(T9,SRF) ∘ P,
(IQ,S3) ∘ P,
(T6IQ,S7RF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T4I,S5R) ∘ P,
(T10I,SF) ∘ P,
(TQ,S7F) ∘ P,
(T7Q,S11R) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T4I,S7F) ∘ P,
(T10I,S11R) ∘ P,
(TQ,S5R) ∘ P,
(T7Q,SF) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T5,S5RF) ∘ P,
(T11,S) ∘ P,
(T2IQ,S11RF) ∘ P,
(T8IQ,S7) ∘ P.
(T0,S0),
(T6,S10RF),
(T3IQ,S6),
(T9IQ,S4RF),
(T5,S7) ∘ P,
(T11,S11RF) ∘ P,
(T2IQ,S) ∘ P,
(T8IQ,S5RF) ∘ 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) .

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