Distribution of groups in curves of genus 5 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] |
12
|
3 |
12 |
$S_3$ |
[6, 1] |
18
|
1 |
1 |
$C_6$ |
[6, 2] |
6
|
4 |
6 |
$C_8$ |
[8, 1] |
6
|
2 |
6 |
$C_2\times C_4$ |
[8, 2] |
27
|
7 |
27 |
$D_4$ |
[8, 3] |
22
|
3 |
5 |
$Q_8$ |
[8, 4] |
6
|
1 |
3 |
$C_2^3$ |
[8, 5] |
77
|
3 |
77 |
$D_5$ |
[10, 1] |
50
|
1 |
2 |
$C_{10}$ |
[10, 2] |
2
|
1 |
2 |
$C_{11}$ |
[11, 1] |
20
|
2 |
20 |
$C_3:C_4$ |
[12, 1] |
2
|
1 |
2 |
$C_{12}$ |
[12, 2] |
4
|
1 |
4 |
$A_4$ |
[12, 3] |
5
|
2 |
2 |
$D_6$ |
[12, 4] |
15
|
3 |
5 |
$C_2\times C_6$ |
[12, 5] |
12
|
2 |
12 |
$C_{15}$ |
[15, 1] |
4
|
1 |
4 |
$C_2^2:C_4$ |
[16, 3] |
28
|
4 |
20 |
$C_2\times C_8$ |
[16, 5] |
8
|
1 |
8 |
$\OD_{16}$ |
[16, 6] |
2
|
1 |
2 |
$D_8$ |
[16, 7] |
8
|
1 |
1 |
$\SD_{16}$ |
[16, 8] |
8
|
1 |
1 |
$C_2^2\times C_4$ |
[16, 10] |
48
|
1 |
48 |
$C_2\times D_4$ |
[16, 11] |
22
|
3 |
11 |
$D_4:C_2$ |
[16, 13] |
6
|
1 |
3 |
$C_2^4$ |
[16, 14] |
168
|
1 |
168 |
$C_5:C_4$ |
[20, 1] |
4
|
1 |
4 |
$C_{20}$ |
[20, 2] |
4
|
1 |
4 |
$D_{10}$ |
[20, 4] |
4
|
1 |
4 |
$C_{22}$ |
[22, 2] |
10
|
1 |
10 |
$C_6:C_4$ |
[24, 7] |
4
|
1 |
4 |
$C_3:D_4$ |
[24, 8] |
4
|
1 |
2 |
$C_2\times C_{12}$ |
[24, 9] |
8
|
1 |
8 |
$S_4$ |
[24, 12] |
6
|
1 |
1 |
$C_2\times A_4$ |
[24, 13] |
6
|
3 |
4 |
$C_2\times D_6$ |
[24, 14] |
12
|
1 |
12 |
$C_3\times D_5$ |
[30, 2] |
4
|
1 |
4 |
$C_2.C_4^2$ |
[32, 2] |
16
|
1 |
16 |
$C_2^2:C_8$ |
[32, 5] |
8
|
1 |
8 |
$C_2^3:C_4$ |
[32, 6] |
2
|
1 |
2 |
$\OD_{16}:C_2$ |
[32, 7] |
4
|
1 |
4 |
$C_2^2\wr C_2$ |
[32, 27] |
24
|
1 |
12 |
$C_4:D_4$ |
[32, 28] |
8
|
1 |
4 |
$D_8:C_2$ |
[32, 43] |
4
|
1 |
1 |
$C_4\times D_5$ |
[40, 5] |
8
|
1 |
8 |
$D_6:C_4$ |
[48, 14] |
8
|
1 |
8 |
$A_4:C_4$ |
[48, 30] |
3
|
2 |
3 |
$C_2\times S_4$ |
[48, 48] |
3
|
1 |
1 |
$C_2^2\times A_4$ |
[48, 49] |
6
|
1 |
6 |
$A_5$ |
[60, 5] |
2
|
1 |
2 |
$C_2^2.D_8$ |
[64, 8] |
8
|
1 |
8 |
$C_2\wr C_4$ |
[64, 32] |
4
|
1 |
4 |
$C_2^4:C_5$ |
[80, 49] |
6
|
1 |
6 |
$C_2^3.A_4$ |
[96, 3] |
4
|
1 |
4 |
$\GL(2,\mathbb{Z}/4)$ |
[96, 195] |
2
|
1 |
2 |
$C_2\times A_5$ |
[120, 35] |
2
|
1 |
2 |
$C_2^4:D_5$ |
[160, 234] |
6
|
1 |
6 |
$C_2^3.S_4$ |
[192, 181] |
4
|
1 |
4 |