Distribution of groups in curves of genus 2 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] |
1
|
1 |
1 |
$C_4$ |
[4, 1] |
1
|
1 |
1 |
$C_2^2$ |
[4, 2] |
3
|
1 |
3 |
$C_5$ |
[5, 1] |
4
|
1 |
4 |
$S_3$ |
[6, 1] |
2
|
1 |
1 |
$C_6$ |
[6, 2] |
3
|
2 |
3 |
$C_8$ |
[8, 1] |
2
|
1 |
2 |
$D_4$ |
[8, 3] |
1
|
1 |
1 |
$Q_8$ |
[8, 4] |
1
|
1 |
1 |
$C_{10}$ |
[10, 2] |
4
|
1 |
4 |
$C_3:C_4$ |
[12, 1] |
1
|
1 |
1 |
$D_6$ |
[12, 4] |
1
|
1 |
1 |
$C_2\times C_6$ |
[12, 5] |
6
|
1 |
6 |
$\SD_{16}$ |
[16, 8] |
2
|
1 |
2 |
$\SL(2,3)$ |
[24, 3] |
1
|
1 |
1 |
$C_3:D_4$ |
[24, 8] |
2
|
1 |
2 |
$\GL(2,3)$ |
[48, 29] |
2
|
1 |
2 |
Distribution of groups in curves of genus 2 with quotient genus greater than 0