Distribution of groups in curves of genus 11 with quotient genus 0
Isomorphism class |
GAP/Magma Group |
Distinct generating vectors |
$C_2$ |
[2, 1] |
1
|
$C_3$ |
[3, 1] |
4
|
$C_4$ |
[4, 1] |
14
|
$C_2^2$ |
[4, 2] |
33
|
$S_3$ |
[6, 1] |
1602
|
$C_6$ |
[6, 2] |
31
|
$C_8$ |
[8, 1] |
27
|
$C_2\times C_4$ |
[8, 2] |
159
|
$D_4$ |
[8, 3] |
286
|
$Q_8$ |
[8, 4] |
62
|
$C_2^3$ |
[8, 5] |
525
|
$C_9$ |
[9, 1] |
24
|
$D_5$ |
[10, 1] |
7812
|
$C_{10}$ |
[10, 2] |
24
|
$C_3:C_4$ |
[12, 1] |
41
|
$C_{12}$ |
[12, 2] |
29
|
$A_4$ |
[12, 3] |
48
|
$D_6$ |
[12, 4] |
257
|
$C_2\times C_6$ |
[12, 5] |
69
|
$C_{15}$ |
[15, 1] |
16
|
$C_{16}$ |
[16, 1] |
20
|
$C_4^2$ |
[16, 2] |
96
|
$C_4:C_4$ |
[16, 4] |
24
|
$C_2\times C_8$ |
[16, 5] |
64
|
$\OD_{16}$ |
[16, 6] |
22
|
$D_8$ |
[16, 7] |
28
|
$\SD_{16}$ |
[16, 8] |
28
|
$Q_{16}$ |
[16, 9] |
12
|
$C_2\times D_4$ |
[16, 11] |
212
|
$C_2\times Q_8$ |
[16, 12] |
20
|
$D_4:C_2$ |
[16, 13] |
89
|
$C_{18}$ |
[18, 2] |
6
|
$C_5:C_4$ |
[20, 1] |
40
|
$C_{20}$ |
[20, 2] |
8
|
$F_5$ |
[20, 3] |
82
|
$D_{10}$ |
[20, 4] |
660
|
$D_{11}$ |
[22, 1] |
605
|
$C_{22}$ |
[22, 2] |
5
|
$C_{23}$ |
[23, 1] |
88
|
$C_{24}$ |
[24, 2] |
12
|
$\SL(2,3)$ |
[24, 3] |
12
|
$C_4\times S_3$ |
[24, 5] |
20
|
$D_{12}$ |
[24, 6] |
48
|
$C_6:C_4$ |
[24, 7] |
20
|
$C_3:D_4$ |
[24, 8] |
12
|
$C_2\times C_{12}$ |
[24, 9] |
36
|
$C_3\times D_4$ |
[24, 10] |
4
|
$S_4$ |
[24, 12] |
32
|
$C_2\times A_4$ |
[24, 13] |
21
|
$C_2\times D_6$ |
[24, 14] |
144
|
$C_3\times D_5$ |
[30, 2] |
12
|
$D_{15}$ |
[30, 3] |
216
|
$C_{30}$ |
[30, 4] |
8
|
$D_4:C_4$ |
[32, 9] |
24
|
$C_4\wr C_2$ |
[32, 11] |
12
|
$C_8.C_4$ |
[32, 15] |
8
|
$C_2\times C_{16}$ |
[32, 16] |
16
|
$\OD_{32}$ |
[32, 17] |
4
|
$C_2\times D_8$ |
[32, 39] |
16
|
$C_2\times \SD_{16}$ |
[32, 40] |
16
|
$D_8:C_2$ |
[32, 42] |
12
|
$D_8:C_2$ |
[32, 43] |
8
|
$Q_{16}:C_2$ |
[32, 44] |
4
|
$C_{33}$ |
[33, 1] |
10
|
$C_5:C_8$ |
[40, 3] |
6
|
$C_4\times D_5$ |
[40, 5] |
48
|
$D_{20}$ |
[40, 6] |
48
|
$C_5:D_4$ |
[40, 8] |
48
|
$C_2\times F_5$ |
[40, 12] |
30
|
$C_2\times D_{10}$ |
[40, 13] |
144
|
$C_{11}:C_4$ |
[44, 1] |
10
|
$C_{44}$ |
[44, 2] |
10
|
$D_{22}$ |
[44, 3] |
10
|
$C_{46}$ |
[46, 2] |
22
|
$C_{12}:C_4$ |
[48, 11] |
16
|
$C_6.D_4$ |
[48, 12] |
8
|
$C_{12}:C_4$ |
[48, 13] |
8
|
$C_2\times C_{24}$ |
[48, 23] |
16
|
$C_3\times \OD_{16}$ |
[48, 24] |
4
|
$C_2.S_4$ |
[48, 28] |
1
|
$\GL(2,3)$ |
[48, 29] |
14
|
$C_2\times \SL(2,3)$ |
[48, 32] |
8
|
$C_2\times D_{12}$ |
[48, 36] |
16
|
$D_{12}:C_2$ |
[48, 37] |
4
|
$S_3\times D_4$ |
[48, 38] |
4
|
$C_2\times S_4$ |
[48, 48] |
8
|
$A_5$ |
[60, 5] |
18
|
$C_3\times F_5$ |
[60, 6] |
2
|
$C_{15}:C_4$ |
[60, 7] |
4
|
$S_3\times D_5$ |
[60, 8] |
12
|
$C_4.D_8$ |
[64, 40] |
8
|
$\OD_{32}:C_2$ |
[64, 42] |
8
|
$C_3\times D_{11}$ |
[66, 2] |
10
|
$D_5:C_8$ |
[80, 28] |
8
|
$C_{20}.C_4$ |
[80, 29] |
4
|
$C_4\times F_5$ |
[80, 30] |
8
|
$C_{20}:C_4$ |
[80, 31] |
4
|
$D_4\times D_5$ |
[80, 39] |
24
|
$D_{20}:C_2$ |
[80, 42] |
24
|
$C_4\times D_{11}$ |
[88, 4] |
20
|
$D_{12}:C_4$ |
[96, 28] |
16
|
$D_{12}:C_4$ |
[96, 32] |
8
|
$C_2\times \GL(2,3)$ |
[96, 189] |
8
|
$\GL(2,3):C_2$ |
[96, 190] |
2
|
$S_5$ |
[120, 34] |
2
|
$C_2\times A_5$ |
[120, 35] |
18
|
$S_3\times F_5$ |
[120, 36] |
2
|
$D_{20}:C_4$ |
[160, 82] |
8
|
$D_{20}:C_4$ |
[160, 85] |
8
|
$C_2\times S_5$ |
[240, 189] |
2
|