Orbit numbers of finite group actions on
Number | Orbit Numbers of non-regular points | OC Satisfied? | |||
---|---|---|---|---|---|
1 | Trivial | 1 | 1 | 1 | all b |
2 | 1, 1 | n | 1 | all b | |
3 | 2, 2n, 2n | 2n | 2 | b even | |
4 | 2, 2n + 1, 2n + 1 | 4n + 2 | 1 | all b | |
5 | A4 | 4, 4, 6 | 6 | 2 | b even |
6 | S4 | 6, 8, 12 | 12 | 2 | b even |
7 | A5 | 6, 10, 15 | 30 | 1 | all b |
8 | 1 | 2 | 1 | all b | |
9 | 2, n | 2n | 2 | b even | |
10 | 2, 2n + 1 | 4n + 2 | 1 | all b | |
11 | 1, 1 | 2n | 1 | all b | |
12 | 2, 2n, 2n | 4n | 2 | b even | |
13 | 2, 2n + 1, 2n + 1 | 8n + 4 | 1 | all b | |
14 | 4, 4, 6 | 12 | 2 | b even | |
15 | 6, 8, 12 | 24 | 2 | b even | |
16 | 6, 10, 15 | 60 | 2 | b even | |
17 | 2, 4n | 4n | 2 | b even | |
18 | 2, 4n + 2 | 4n + 2 | 2 | b even | |
19 | 6, 8 | 12 | 2 | b even | |
20 | − | 1 | 2 | b even | |
21 | 2 | n | 2 | b even |