Distribution of groups in curves of genus 3 with quotient genus 0
| Isomorphism class |
GAP/Magma Group |
Distinct generating vectors |
Topologically inequivalent actions |
Braid inequivalent actions |
| $C_2$ |
[2, 1] |
1
|
1 |
1 |
| $C_3$ |
[3, 1] |
2
|
1 |
2 |
| $C_4$ |
[4, 1] |
5
|
3 |
5 |
| $C_2^2$ |
[4, 2] |
7
|
2 |
7 |
| $S_3$ |
[6, 1] |
9
|
1 |
1 |
| $C_6$ |
[6, 2] |
3
|
2 |
3 |
| $C_7$ |
[7, 1] |
8
|
2 |
8 |
| $C_8$ |
[8, 1] |
6
|
2 |
6 |
| $C_2\times C_4$ |
[8, 2] |
12
|
3 |
12 |
| $D_4$ |
[8, 3] |
6
|
2 |
3 |
| $C_2^3$ |
[8, 5] |
28
|
1 |
28 |
| $C_9$ |
[9, 1] |
6
|
1 |
6 |
| $C_3:C_4$ |
[12, 1] |
2
|
1 |
2 |
| $C_{12}$ |
[12, 2] |
6
|
2 |
6 |
| $A_4$ |
[12, 3] |
3
|
1 |
1 |
| $D_6$ |
[12, 4] |
2
|
1 |
2 |
| $C_{14}$ |
[14, 2] |
6
|
1 |
6 |
| $C_4^2$ |
[16, 2] |
16
|
1 |
16 |
| $C_4:C_4$ |
[16, 4] |
4
|
1 |
4 |
| $C_2\times C_8$ |
[16, 5] |
8
|
1 |
8 |
| $\OD_{16}$ |
[16, 6] |
2
|
1 |
2 |
| $C_2\times D_4$ |
[16, 11] |
8
|
1 |
8 |
| $D_4:C_2$ |
[16, 13] |
2
|
1 |
2 |
| $C_7:C_3$ |
[21, 1] |
2
|
1 |
2 |
| $\SL(2,3)$ |
[24, 3] |
2
|
1 |
2 |
| $C_4\times S_3$ |
[24, 5] |
4
|
1 |
4 |
| $S_4$ |
[24, 12] |
4
|
2 |
2 |
| $C_2\times A_4$ |
[24, 13] |
1
|
1 |
1 |
| $D_4:C_4$ |
[32, 9] |
8
|
1 |
8 |
| $C_4\wr C_2$ |
[32, 11] |
4
|
1 |
4 |
| $C_4^2:C_3$ |
[48, 3] |
4
|
1 |
4 |
| $\SL(2,3):C_2$ |
[48, 33] |
4
|
1 |
4 |
| $C_2\times S_4$ |
[48, 48] |
2
|
1 |
2 |
| $C_4^2:S_3$ |
[96, 64] |
2
|
1 |
2 |
| $\GL(3,2)$ |
[168, 42] |
2
|
1 |
2 |
Distribution of groups in curves of genus 3 with quotient genus greater than 0
