Stabilizer type Y

Acting group: 𝔄12
There are exactly 144 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(TI,R),
(T,SR) ∘ P,
(I,S11) ∘ P.
(T0,S0),
(TI,R),
(T3Q,S3RF) ∘ P,
(T10IQ,S9F) ∘ P.
(T0,S0),
(TI,R),
(T7,S7R) ∘ P,
(T6I,S5) ∘ P.
(T0,S0),
(TI,R),
(T9Q,S9RF) ∘ P,
(T4IQ,S3F) ∘ P.
(T0,S0),
(TI,S2R),
(T0,S2R) ∘ P,
(TI,S0) ∘ P.
(T0,S0),
(TI,S2R),
(T4Q,S10RF) ∘ P,
(T9IQ,S4F) ∘ P.
(T0,S0),
(TI,S2R),
(T6,S8R) ∘ P,
(T7I,S6) ∘ P.
(T0,S0),
(TI,S2R),
(T10Q,S4RF) ∘ P,
(T3IQ,S10F) ∘ P.
(T0,S0),
(TI,S4R),
(T5,S9R) ∘ P,
(T8I,S7) ∘ P.
(T0,S0),
(TI,S4R),
(T5Q,S5RF) ∘ P,
(T8IQ,S11F) ∘ P.
(T0,S0),
(TI,S4R),
(T11,S3R) ∘ P,
(T2I,S) ∘ P.
(T0,S0),
(TI,S4R),
(T11Q,S11RF) ∘ P,
(T2IQ,S5F) ∘ P.
(T0,S0),
(TI,S6R),
(Q,S6RF) ∘ P,
(TIQ,F) ∘ P.
(T0,S0),
(TI,S6R),
(T4,S10R) ∘ P,
(T9I,S8) ∘ P.
(T0,S0),
(TI,S6R),
(T6Q,RF) ∘ P,
(T7IQ,S6F) ∘ P.
(T0,S0),
(TI,S6R),
(T10,S4R) ∘ P,
(T3I,S2) ∘ P.
(T0,S0),
(TI,S8R),
(TQ,SRF) ∘ P,
(IQ,S7F) ∘ P.
(T0,S0),
(TI,S8R),
(T3,S11R) ∘ P,
(T10I,S9) ∘ P.
(T0,S0),
(TI,S8R),
(T7Q,S7RF) ∘ P,
(T6IQ,SF) ∘ P.
(T0,S0),
(TI,S8R),
(T9,S5R) ∘ P,
(T4I,S3) ∘ P.
(T0,S0),
(TI,S10R),
(T2,R) ∘ P,
(T11I,S10) ∘ P.
(T0,S0),
(TI,S10R),
(T2Q,S8RF) ∘ P,
(T11IQ,S2F) ∘ P.
(T0,S0),
(TI,S10R),
(T8,S6R) ∘ P,
(T5I,S4) ∘ P.
(T0,S0),
(TI,S10R),
(T8Q,S2RF) ∘ P,
(T5IQ,S8F) ∘ P.
(T0,S0),
(T3I,R),
(T2,S2R) ∘ P,
(TI,S10) ∘ P.
(T0,S0),
(T3I,R),
(T4Q,S8RF) ∘ P,
(T11IQ,S4F) ∘ P.
(T0,S0),
(T3I,R),
(T8,S8R) ∘ P,
(T7I,S4) ∘ P.
(T0,S0),
(T3I,R),
(T10Q,S2RF) ∘ P,
(T5IQ,S10F) ∘ P.
(T0,S0),
(T3I,S2R),
(T,S3R) ∘ P,
(T2I,S11) ∘ P.
(T0,S0),
(T3I,S2R),
(T5Q,S3RF) ∘ P,
(T10IQ,S11F) ∘ P.
(T0,S0),
(T3I,S2R),
(T7,S9R) ∘ P,
(T8I,S5) ∘ P.
(T0,S0),
(T3I,S2R),
(T11Q,S9RF) ∘ P,
(T4IQ,S5F) ∘ P.
(T0,S0),
(T3I,S4R),
(T0,S4R) ∘ P,
(T3I,S0) ∘ P.
(T0,S0),
(T3I,S4R),
(Q,S4RF) ∘ P,
(T3IQ,F) ∘ P.
(T0,S0),
(T3I,S4R),
(T6,S10R) ∘ P,
(T9I,S6) ∘ P.
(T0,S0),
(T3I,S4R),
(T6Q,S10RF) ∘ P,
(T9IQ,S6F) ∘ P.
(T0,S0),
(T3I,S6R),
(TQ,S11RF) ∘ P,
(T2IQ,S7F) ∘ P.
(T0,S0),
(T3I,S6R),
(T5,S11R) ∘ P,
(T10I,S7) ∘ P.
(T0,S0),
(T3I,S6R),
(T7Q,S5RF) ∘ P,
(T8IQ,SF) ∘ P.
(T0,S0),
(T3I,S6R),
(T11,S5R) ∘ P,
(T4I,S) ∘ P.
(T0,S0),
(T3I,S8R),
(T2Q,S6RF) ∘ P,
(TIQ,S2F) ∘ P.
(T0,S0),
(T3I,S8R),
(T4,R) ∘ P,
(T11I,S8) ∘ P.
(T0,S0),
(T3I,S8R),
(T8Q,RF) ∘ P,
(T7IQ,S8F) ∘ P.
(T0,S0),
(T3I,S8R),
(T10,S6R) ∘ P,
(T5I,S2) ∘ P.
(T0,S0),
(T3I,S10R),
(T3,SR) ∘ P,
(I,S9) ∘ P.
(T0,S0),
(T3I,S10R),
(T3Q,SRF) ∘ P,
(IQ,S9F) ∘ P.
(T0,S0),
(T3I,S10R),
(T9,S7R) ∘ P,
(T6I,S3) ∘ P.
(T0,S0),
(T3I,S10R),
(T9Q,S7RF) ∘ P,
(T6IQ,S3F) ∘ P.
(T0,S0),
(T5I,R),
(T3,S3R) ∘ P,
(T2I,S9) ∘ P.
(T0,S0),
(T5I,R),
(T5Q,SRF) ∘ P,
(IQ,S11F) ∘ P.
(T0,S0),
(T5I,R),
(T9,S9R) ∘ P,
(T8I,S3) ∘ P.
(T0,S0),
(T5I,R),
(T11Q,S7RF) ∘ P,
(T6IQ,S5F) ∘ P.
(T0,S0),
(T5I,S2R),
(Q,S2RF) ∘ P,
(T5IQ,F) ∘ P.
(T0,S0),
(T5I,S2R),
(T2,S4R) ∘ P,
(T3I,S10) ∘ P.
(T0,S0),
(T5I,S2R),
(T6Q,S8RF) ∘ P,
(T11IQ,S6F) ∘ P.
(T0,S0),
(T5I,S2R),
(T8,S10R) ∘ P,
(T9I,S4) ∘ P.
(T0,S0),
(T5I,S4R),
(T,S5R) ∘ P,
(T4I,S11) ∘ P.
(T0,S0),
(T5I,S4R),
(TQ,S9RF) ∘ P,
(T4IQ,S7F) ∘ P.
(T0,S0),
(T5I,S4R),
(T7,S11R) ∘ P,
(T10I,S5) ∘ P.
(T0,S0),
(T5I,S4R),
(T7Q,S3RF) ∘ P,
(T10IQ,SF) ∘ P.
(T0,S0),
(T5I,S6R),
(T0,S6R) ∘ P,
(T5I,S0) ∘ P.
(T0,S0),
(T5I,S6R),
(T2Q,S4RF) ∘ P,
(T3IQ,S2F) ∘ P.
(T0,S0),
(T5I,S6R),
(T6,R) ∘ P,
(T11I,S6) ∘ P.
(T0,S0),
(T5I,S6R),
(T8Q,S10RF) ∘ P,
(T9IQ,S8F) ∘ P.
(T0,S0),
(T5I,S8R),
(T3Q,S11RF) ∘ P,
(T2IQ,S9F) ∘ P.
(T0,S0),
(T5I,S8R),
(T5,SR) ∘ P,
(I,S7) ∘ P.
(T0,S0),
(T5I,S8R),
(T9Q,S5RF) ∘ P,
(T8IQ,S3F) ∘ P.
(T0,S0),
(T5I,S8R),
(T11,S7R) ∘ P,
(T6I,S) ∘ P.
(T0,S0),
(T5I,S10R),
(T4,S2R) ∘ P,
(TI,S8) ∘ P.
(T0,S0),
(T5I,S10R),
(T4Q,S6RF) ∘ P,
(TIQ,S4F) ∘ P.
(T0,S0),
(T5I,S10R),
(T10,S8R) ∘ P,
(T7I,S2) ∘ P.
(T0,S0),
(T5I,S10R),
(T10Q,RF) ∘ P,
(T7IQ,S10F) ∘ P.
(T0,S0),
(T7I,R),
(Q,RF) ∘ P,
(T7IQ,F) ∘ P.
(T0,S0),
(T7I,R),
(T4,S4R) ∘ P,
(T3I,S8) ∘ P.
(T0,S0),
(T7I,R),
(T6Q,S6RF) ∘ P,
(TIQ,S6F) ∘ P.
(T0,S0),
(T7I,R),
(T10,S10R) ∘ P,
(T9I,S2) ∘ P.
(T0,S0),
(T7I,S2R),
(TQ,S7RF) ∘ P,
(T6IQ,S7F) ∘ P.
(T0,S0),
(T7I,S2R),
(T3,S5R) ∘ P,
(T4I,S9) ∘ P.
(T0,S0),
(T7I,S2R),
(T7Q,SRF) ∘ P,
(IQ,SF) ∘ P.
(T0,S0),
(T7I,S2R),
(T9,S11R) ∘ P,
(T10I,S3) ∘ P.
(T0,S0),
(T7I,S4R),
(T2,S6R) ∘ P,
(T5I,S10) ∘ P.
(T0,S0),
(T7I,S4R),
(T2Q,S2RF) ∘ P,
(T5IQ,S2F) ∘ P.
(T0,S0),
(T7I,S4R),
(T8,R) ∘ P,
(T11I,S4) ∘ P.
(T0,S0),
(T7I,S4R),
(T8Q,S8RF) ∘ P,
(T11IQ,S8F) ∘ P.
(T0,S0),
(T7I,S6R),
(T,S7R) ∘ P,
(T6I,S11) ∘ P.
(T0,S0),
(T7I,S6R),
(T3Q,S9RF) ∘ P,
(T4IQ,S9F) ∘ P.
(T0,S0),
(T7I,S6R),
(T7,SR) ∘ P,
(I,S5) ∘ P.
(T0,S0),
(T7I,S6R),
(T9Q,S3RF) ∘ P,
(T10IQ,S3F) ∘ P.
(T0,S0),
(T7I,S8R),
(T0,S8R) ∘ P,
(T7I,S0) ∘ P.
(T0,S0),
(T7I,S8R),
(T4Q,S4RF) ∘ P,
(T3IQ,S4F) ∘ P.
(T0,S0),
(T7I,S8R),
(T6,S2R) ∘ P,
(TI,S6) ∘ P.
(T0,S0),
(T7I,S8R),
(T10Q,S10RF) ∘ P,
(T9IQ,S10F) ∘ P.
(T0,S0),
(T7I,S10R),
(T5,S3R) ∘ P,
(T2I,S7) ∘ P.
(T0,S0),
(T7I,S10R),
(T5Q,S11RF) ∘ P,
(T2IQ,S11F) ∘ P.
(T0,S0),
(T7I,S10R),
(T11,S9R) ∘ P,
(T8I,S) ∘ P.
(T0,S0),
(T7I,S10R),
(T11Q,S5RF) ∘ P,
(T8IQ,S5F) ∘ P.
(T0,S0),
(T9I,R),
(TQ,S5RF) ∘ P,
(T8IQ,S7F) ∘ P.
(T0,S0),
(T9I,R),
(T5,S5R) ∘ P,
(T4I,S7) ∘ P.
(T0,S0),
(T9I,R),
(T7Q,S11RF) ∘ P,
(T2IQ,SF) ∘ P.
(T0,S0),
(T9I,R),
(T11,S11R) ∘ P,
(T10I,S) ∘ P.
(T0,S0),
(T9I,S2R),
(T2Q,RF) ∘ P,
(T7IQ,S2F) ∘ P.
(T0,S0),
(T9I,S2R),
(T4,S6R) ∘ P,
(T5I,S8) ∘ P.
(T0,S0),
(T9I,S2R),
(T8Q,S6RF) ∘ P,
(TIQ,S8F) ∘ P.
(T0,S0),
(T9I,S2R),
(T10,R) ∘ P,
(T11I,S2) ∘ P.
(T0,S0),
(T9I,S4R),
(T3,S7R) ∘ P,
(T6I,S9) ∘ P.
(T0,S0),
(T9I,S4R),
(T3Q,S7RF) ∘ P,
(T6IQ,S9F) ∘ P.
(T0,S0),
(T9I,S4R),
(T9,SR) ∘ P,
(I,S3) ∘ P.
(T0,S0),
(T9I,S4R),
(T9Q,SRF) ∘ P,
(IQ,S3F) ∘ P.
(T0,S0),
(T9I,S6R),
(T2,S8R) ∘ P,
(T7I,S10) ∘ P.
(T0,S0),
(T9I,S6R),
(T4Q,S2RF) ∘ P,
(T5IQ,S4F) ∘ P.
(T0,S0),
(T9I,S6R),
(T8,S2R) ∘ P,
(TI,S4) ∘ P.
(T0,S0),
(T9I,S6R),
(T10Q,S8RF) ∘ P,
(T11IQ,S10F) ∘ P.
(T0,S0),
(T9I,S8R),
(T,S9R) ∘ P,
(T8I,S11) ∘ P.
(T0,S0),
(T9I,S8R),
(T5Q,S9RF) ∘ P,
(T4IQ,S11F) ∘ P.
(T0,S0),
(T9I,S8R),
(T7,S3R) ∘ P,
(T2I,S5) ∘ P.
(T0,S0),
(T9I,S8R),
(T11Q,S3RF) ∘ P,
(T10IQ,S5F) ∘ P.
(T0,S0),
(T9I,S10R),
(T0,S10R) ∘ P,
(T9I,S0) ∘ P.
(T0,S0),
(T9I,S10R),
(Q,S10RF) ∘ P,
(T9IQ,F) ∘ P.
(T0,S0),
(T9I,S10R),
(T6,S4R) ∘ P,
(T3I,S6) ∘ P.
(T0,S0),
(T9I,S10R),
(T6Q,S4RF) ∘ P,
(T3IQ,S6F) ∘ P.
(T0,S0),
(T11I,R),
(T0,R) ∘ P,
(T11I,S0) ∘ P.
(T0,S0),
(T11I,R),
(T2Q,S10RF) ∘ P,
(T9IQ,S2F) ∘ P.
(T0,S0),
(T11I,R),
(T6,S6R) ∘ P,
(T5I,S6) ∘ P.
(T0,S0),
(T11I,R),
(T8Q,S4RF) ∘ P,
(T3IQ,S8F) ∘ P.
(T0,S0),
(T11I,S2R),
(T3Q,S5RF) ∘ P,
(T8IQ,S9F) ∘ P.
(T0,S0),
(T11I,S2R),
(T5,S7R) ∘ P,
(T6I,S7) ∘ P.
(T0,S0),
(T11I,S2R),
(T9Q,S11RF) ∘ P,
(T2IQ,S3F) ∘ P.
(T0,S0),
(T11I,S2R),
(T11,SR) ∘ P,
(I,S) ∘ P.
(T0,S0),
(T11I,S4R),
(T4,S8R) ∘ P,
(T7I,S8) ∘ P.
(T0,S0),
(T11I,S4R),
(T4Q,RF) ∘ P,
(T7IQ,S4F) ∘ P.
(T0,S0),
(T11I,S4R),
(T10,S2R) ∘ P,
(TI,S2) ∘ P.
(T0,S0),
(T11I,S4R),
(T10Q,S6RF) ∘ P,
(TIQ,S10F) ∘ P.
(T0,S0),
(T11I,S6R),
(T3,S9R) ∘ P,
(T8I,S9) ∘ P.
(T0,S0),
(T11I,S6R),
(T5Q,S7RF) ∘ P,
(T6IQ,S11F) ∘ P.
(T0,S0),
(T11I,S6R),
(T9,S3R) ∘ P,
(T2I,S3) ∘ P.
(T0,S0),
(T11I,S6R),
(T11Q,SRF) ∘ P,
(IQ,S5F) ∘ P.
(T0,S0),
(T11I,S8R),
(Q,S8RF) ∘ P,
(T11IQ,F) ∘ P.
(T0,S0),
(T11I,S8R),
(T2,S10R) ∘ P,
(T9I,S10) ∘ P.
(T0,S0),
(T11I,S8R),
(T6Q,S2RF) ∘ P,
(T5IQ,S6F) ∘ P.
(T0,S0),
(T11I,S8R),
(T8,S4R) ∘ P,
(T3I,S4) ∘ P.
(T0,S0),
(T11I,S10R),
(T,S11R) ∘ P,
(T10I,S11) ∘ P.
(T0,S0),
(T11I,S10R),
(TQ,S3RF) ∘ P,
(T10IQ,S7F) ∘ P.
(T0,S0),
(T11I,S10R),
(T7,S5R) ∘ P,
(T4I,S5) ∘ P.
(T0,S0),
(T11I,S10R),
(T7Q,S9RF) ∘ P,
(T4IQ,SF) ∘ 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