How to input the stabilizer type of
Aff1(Z12) × D12-orbits
There are 29 different conjugacy classes of subgroups of
Aff1(Z12) × D12 which occur
as stabilizers of tone rows. Prescribe the stabilizer type by
choosing a number from 1 to 29.
| name |
generators |
size of the group |
size of the class |
number of orbits |
| W1 |
identity |
1 |
1 |
412326 |
| W2 |
(TI,R) |
2 |
36 |
|
| W3 |
(I,SR) |
2 |
36 |
|
| W4 |
(TI,S6) |
2 |
6 |
|
| W5 |
(T6,R) |
2 |
6 |
|
| W6 |
(T2Q,R) |
2 |
18 |
|
| W7 |
(T3IQ,R) |
2 |
12 |
|
| W8 |
(T6,S6) |
2 |
1 |
|
| W9 |
(T2Q,S6) |
2 |
3 |
|
| W10 |
(T3IQ,S6) |
2 |
2 |
|
| W11 |
(T4,S4) |
3 |
2 |
|
| W12 |
(TI,S6),
(T6,R) |
4 |
36 |
|
| W13 |
(I,SR),
(T6,S6) |
4 |
18 |
|
| W14 |
(TI,R),
(T6,S6) |
4 |
18 |
|
| W15 |
(TI,R),
(T3IQ,S6) |
4 |
36 |
|
| W16 |
(TI,R),
(T10Q,S6) |
4 |
36 |
|
| W17 |
(TI,S6),
(T10Q,R) |
4 |
36 |
|
| W18 |
(T6,R),
(T3IQ,S6) |
4 |
12 |
|
| W19 |
(TQ,S3) |
4 |
6 |
|
| W20 |
(T6,S6),
(T3IQ,R) |
4 |
6 |
|
| W21 |
(T3,S3) |
4 |
2 |
|
| W22 |
(TI,R),
(T4,S4) |
6 |
24 |
|
| W23 |
(I,SR),
(T4,S4) |
6 |
24 |
|
| W24 |
(T4,S4),
(T2Q,R) |
6 |
12 |
|
| W25 |
(I,SR),
(T3Q,S3) |
8 |
36 |
|
| W26 |
(I,SR),
(T3,S3) |
8 |
36 |
|
| W27 |
(TI,R),
(T7IQ,S2) |
12 |
24 |
|
| W28 |
(TI,R),
(T2,S2) |
12 |
12 |
|
| W29 |
(I,SR), (T,S) |
24 |
24 |
|
Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019