How to input the stabilizer type of D12 ×
Aff1(Z12)-orbits
There are 29 different conjugacy classes of subgroups of
D12 × Aff1(Z12) 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 |
| W'1 |
identity |
1 |
1 |
412326 |
| W'2 |
(TI,R) |
2 |
36 |
|
| W'3 |
(I,SR) |
2 |
36 |
|
| W'4 |
(TI,S6) |
2 |
6 |
|
| W'5 |
(T6,R) |
2 |
6 |
|
| W'6 |
(TI,S2F) |
2 |
18 |
|
| W'7 |
(T6,S6) |
2 |
1 |
|
| W'8 |
(TI,S4RF) |
2 |
12 |
|
| W'9 |
(T6,S4RF) |
2 |
2 |
|
| W'10 |
(T6,S2F) |
2 |
3 |
|
| W'11 |
(T4,S4) |
3 |
2 |
|
| W'12 |
(TI,S6),
(T6,R) |
4 |
36 |
|
| W'13 |
(I,SR),
(T6,S6) |
4 |
18 |
|
| W'14 |
(TI,R),
(T6,S6) |
4 |
18 |
|
| W'15 |
(TI,R),
(T7I,S2F) |
4 |
36 |
|
| W'16 |
(TI,R),
(T6,S2F) |
4 |
36 |
|
| W'17 |
(T6,R),
(TI,S2F) |
4 |
36 |
|
| W'18 |
(TI,S6),
(T6,S4RF) |
4 |
12 |
|
| W'19 |
(T6,S6),
(TI,S4RF) |
4 |
6 |
|
| W'20 |
(T3,SF) |
4 |
6 |
|
| W'21 |
(T3,S3) |
4 |
2 |
|
| W'22 |
(TI,R),
(T4,S4) |
6 |
24 |
|
| W'23 |
(I,SR),
(T4,S4) |
6 |
24 |
|
| W'24 |
(T4,S4),
(TI,S2F) |
6 |
12 |
|
| W'25 |
(I,SR),
(T3,S3F) |
8 |
36 |
|
| W'26 |
(I,SR),
(T3,S3) |
8 |
36 |
|
| W'27 |
(TI,R),
(T2,S6RF) |
12 |
24 |
|
| W'28 |
(TI,R),
(T2,S2) |
12 |
12 |
|
| W'29 |
(I,SR), (T,S) |
24 |
24 |
|
Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019