Stabilizer type Y45

Acting group: 𝔄12
There are exactly 72 groups in this conjugacy class.
The group order is 4.
(T0,S0),
(T2Q,S2F),
(T0,S2F) ∘ P,
(T2Q,S0) ∘ P.
(T0,S0),
(T2Q,S2F),
(T2I,SRF) ∘ P,
(IQ,S3R) ∘ P.
(T0,S0),
(T2Q,S2F),
(T3,S11F) ∘ P,
(T5Q,S9) ∘ P.
(T0,S0),
(T2Q,S2F),
(T5I,S4RF) ∘ P,
(T3IQ,S6R) ∘ P.
(T0,S0),
(T2Q,S2F),
(T6,S8F) ∘ P,
(T8Q,S6) ∘ P.
(T0,S0),
(T2Q,S2F),
(T8I,S7RF) ∘ P,
(T6IQ,S9R) ∘ P.
(T0,S0),
(T2Q,S2F),
(T9,S5F) ∘ P,
(T11Q,S3) ∘ P.
(T0,S0),
(T2Q,S2F),
(T11I,S10RF) ∘ P,
(T9IQ,R) ∘ P.
(T0,S0),
(T2Q,S6F),
(T,SF) ∘ P,
(T7Q,S11) ∘ P.
(T0,S0),
(T2Q,S6F),
(TI,RF) ∘ P,
(T7IQ,S2R) ∘ P.
(T0,S0),
(T2Q,S6F),
(T4,S10F) ∘ P,
(T10Q,S8) ∘ P.
(T0,S0),
(T2Q,S6F),
(T4I,S3RF) ∘ P,
(T10IQ,S5R) ∘ P.
(T0,S0),
(T2Q,S6F),
(T7,S7F) ∘ P,
(TQ,S5) ∘ P.
(T0,S0),
(T2Q,S6F),
(T7I,S6RF) ∘ P,
(TIQ,S8R) ∘ P.
(T0,S0),
(T2Q,S6F),
(T10,S4F) ∘ P,
(T4Q,S2) ∘ P.
(T0,S0),
(T2Q,S6F),
(T10I,S9RF) ∘ P,
(T4IQ,S11R) ∘ P.
(T0,S0),
(T2Q,S10F),
(I,S11RF) ∘ P,
(T2IQ,SR) ∘ P.
(T0,S0),
(T2Q,S10F),
(T2,F) ∘ P,
(Q,S10) ∘ P.
(T0,S0),
(T2Q,S10F),
(T3I,S2RF) ∘ P,
(T5IQ,S4R) ∘ P.
(T0,S0),
(T2Q,S10F),
(T5,S9F) ∘ P,
(T3Q,S7) ∘ P.
(T0,S0),
(T2Q,S10F),
(T6I,S5RF) ∘ P,
(T8IQ,S7R) ∘ P.
(T0,S0),
(T2Q,S10F),
(T8,S6F) ∘ P,
(T6Q,S4) ∘ P.
(T0,S0),
(T2Q,S10F),
(T9I,S8RF) ∘ P,
(T11IQ,S10R) ∘ P.
(T0,S0),
(T2Q,S10F),
(T11,S3F) ∘ P,
(T9Q,S) ∘ P.
(T0,S0),
(T6Q,S2F),
(TI,S8RF) ∘ P,
(T11IQ,S2R) ∘ P.
(T0,S0),
(T6Q,S2F),
(T2,S4F) ∘ P,
(T4Q,S10) ∘ P.
(T0,S0),
(T6Q,S2F),
(T4I,S11RF) ∘ P,
(T2IQ,S5R) ∘ P.
(T0,S0),
(T6Q,S2F),
(T5,SF) ∘ P,
(T7Q,S7) ∘ P.
(T0,S0),
(T6Q,S2F),
(T7I,S2RF) ∘ P,
(T5IQ,S8R) ∘ P.
(T0,S0),
(T6Q,S2F),
(T8,S10F) ∘ P,
(T10Q,S4) ∘ P.
(T0,S0),
(T6Q,S2F),
(T10I,S5RF) ∘ P,
(T8IQ,S11R) ∘ P.
(T0,S0),
(T6Q,S2F),
(T11,S7F) ∘ P,
(TQ,S) ∘ P.
(T0,S0),
(T6Q,S6F),
(T0,S6F) ∘ P,
(T6Q,S0) ∘ P.
(T0,S0),
(T6Q,S6F),
(I,S7RF) ∘ P,
(T6IQ,SR) ∘ P.
(T0,S0),
(T6Q,S6F),
(T3,S3F) ∘ P,
(T9Q,S9) ∘ P.
(T0,S0),
(T6Q,S6F),
(T3I,S10RF) ∘ P,
(T9IQ,S4R) ∘ P.
(T0,S0),
(T6Q,S6F),
(T6,F) ∘ P,
(Q,S6) ∘ P.
(T0,S0),
(T6Q,S6F),
(T6I,SRF) ∘ P,
(IQ,S7R) ∘ P.
(T0,S0),
(T6Q,S6F),
(T9,S9F) ∘ P,
(T3Q,S3) ∘ P.
(T0,S0),
(T6Q,S6F),
(T9I,S4RF) ∘ P,
(T3IQ,S10R) ∘ P.
(T0,S0),
(T6Q,S10F),
(T,S5F) ∘ P,
(T11Q,S11) ∘ P.
(T0,S0),
(T6Q,S10F),
(T2I,S9RF) ∘ P,
(T4IQ,S3R) ∘ P.
(T0,S0),
(T6Q,S10F),
(T4,S2F) ∘ P,
(T2Q,S8) ∘ P.
(T0,S0),
(T6Q,S10F),
(T5I,RF) ∘ P,
(T7IQ,S6R) ∘ P.
(T0,S0),
(T6Q,S10F),
(T7,S11F) ∘ P,
(T5Q,S5) ∘ P.
(T0,S0),
(T6Q,S10F),
(T8I,S3RF) ∘ P,
(T10IQ,S9R) ∘ P.
(T0,S0),
(T6Q,S10F),
(T10,S8F) ∘ P,
(T8Q,S2) ∘ P.
(T0,S0),
(T6Q,S10F),
(T11I,S6RF) ∘ P,
(TIQ,R) ∘ P.
(T0,S0),
(T10Q,S2F),
(I,S3RF) ∘ P,
(T10IQ,SR) ∘ P.
(T0,S0),
(T10Q,S2F),
(T,S9F) ∘ P,
(T3Q,S11) ∘ P.
(T0,S0),
(T10Q,S2F),
(T3I,S6RF) ∘ P,
(TIQ,S4R) ∘ P.
(T0,S0),
(T10Q,S2F),
(T4,S6F) ∘ P,
(T6Q,S8) ∘ P.
(T0,S0),
(T10Q,S2F),
(T6I,S9RF) ∘ P,
(T4IQ,S7R) ∘ P.
(T0,S0),
(T10Q,S2F),
(T7,S3F) ∘ P,
(T9Q,S5) ∘ P.
(T0,S0),
(T10Q,S2F),
(T9I,RF) ∘ P,
(T7IQ,S10R) ∘ P.
(T0,S0),
(T10Q,S2F),
(T10,F) ∘ P,
(Q,S2) ∘ P.
(T0,S0),
(T10Q,S6F),
(T2,S8F) ∘ P,
(T8Q,S10) ∘ P.
(T0,S0),
(T10Q,S6F),
(T2I,S5RF) ∘ P,
(T8IQ,S3R) ∘ P.
(T0,S0),
(T10Q,S6F),
(T5,S5F) ∘ P,
(T11Q,S7) ∘ P.
(T0,S0),
(T10Q,S6F),
(T5I,S8RF) ∘ P,
(T11IQ,S6R) ∘ P.
(T0,S0),
(T10Q,S6F),
(T8,S2F) ∘ P,
(T2Q,S4) ∘ P.
(T0,S0),
(T10Q,S6F),
(T8I,S11RF) ∘ P,
(T2IQ,S9R) ∘ P.
(T0,S0),
(T10Q,S6F),
(T11,S11F) ∘ P,
(T5Q,S) ∘ P.
(T0,S0),
(T10Q,S6F),
(T11I,S2RF) ∘ P,
(T5IQ,R) ∘ P.
(T0,S0),
(T10Q,S10F),
(T0,S10F) ∘ P,
(T10Q,S0) ∘ P.
(T0,S0),
(T10Q,S10F),
(TI,S4RF) ∘ P,
(T3IQ,S2R) ∘ P.
(T0,S0),
(T10Q,S10F),
(T3,S7F) ∘ P,
(TQ,S9) ∘ P.
(T0,S0),
(T10Q,S10F),
(T4I,S7RF) ∘ P,
(T6IQ,S5R) ∘ P.
(T0,S0),
(T10Q,S10F),
(T6,S4F) ∘ P,
(T4Q,S6) ∘ P.
(T0,S0),
(T10Q,S10F),
(T7I,S10RF) ∘ P,
(T9IQ,S8R) ∘ P.
(T0,S0),
(T10Q,S10F),
(T9,SF) ∘ P,
(T7Q,S3) ∘ P.
(T0,S0),
(T10Q,S10F),
(T10I,SRF) ∘ P,
(IQ,S11R) ∘ 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