Distribution of groups in curves of genus 12 with quotient genus 0
Isomorphism class |
GAP/Magma Group |
Distinct generating vectors |
$C_2$ |
[2, 1] |
1
|
$C_3$ |
[3, 1] |
5
|
$C_4$ |
[4, 1] |
15
|
$C_2^2$ |
[4, 2] |
28
|
$C_5$ |
[5, 1] |
33
|
$S_3$ |
[6, 1] |
7273
|
$C_6$ |
[6, 2] |
40
|
$C_7$ |
[7, 1] |
66
|
$C_8$ |
[8, 1] |
34
|
$D_4$ |
[8, 3] |
365
|
$Q_8$ |
[8, 4] |
13
|
$C_9$ |
[9, 1] |
45
|
$D_5$ |
[10, 1] |
40
|
$C_{10}$ |
[10, 2] |
55
|
$C_3:C_4$ |
[12, 1] |
25
|
$C_{12}$ |
[12, 2] |
47
|
$A_4$ |
[12, 3] |
209
|
$D_6$ |
[12, 4] |
312
|
$C_2\times C_6$ |
[12, 5] |
65
|
$C_{13}$ |
[13, 1] |
105
|
$D_7$ |
[14, 1] |
40
|
$C_{14}$ |
[14, 2] |
71
|
$C_{15}$ |
[15, 1] |
48
|
$C_{16}$ |
[16, 1] |
16
|
$D_8$ |
[16, 7] |
74
|
$\SD_{16}$ |
[16, 8] |
4
|
$Q_{16}$ |
[16, 9] |
2
|
$D_9$ |
[18, 1] |
12
|
$C_{18}$ |
[18, 2] |
27
|
$C_5:C_4$ |
[20, 1] |
6
|
$C_{20}$ |
[20, 2] |
10
|
$F_5$ |
[20, 3] |
4
|
$D_{10}$ |
[20, 4] |
6
|
$C_2\times C_{10}$ |
[20, 5] |
38
|
$C_7:C_3$ |
[21, 1] |
9
|
$C_{21}$ |
[21, 2] |
3
|
$D_{11}$ |
[22, 1] |
7320
|
$C_3:C_8$ |
[24, 1] |
2
|
$C_{24}$ |
[24, 2] |
4
|
$\SL(2,3)$ |
[24, 3] |
9
|
$C_3:Q_8$ |
[24, 4] |
4
|
$D_{12}$ |
[24, 6] |
148
|
$C_3:D_4$ |
[24, 8] |
6
|
$C_3\times D_4$ |
[24, 10] |
10
|
$S_4$ |
[24, 12] |
45
|
$C_{25}$ |
[25, 1] |
60
|
$D_{13}$ |
[26, 1] |
42
|
$C_{26}$ |
[26, 2] |
78
|
$C_{27}$ |
[27, 1] |
54
|
$C_{28}$ |
[28, 2] |
30
|
$D_{14}$ |
[28, 3] |
18
|
$C_2\times C_{14}$ |
[28, 4] |
48
|
$C_5\times S_3$ |
[30, 1] |
12
|
$D_{15}$ |
[30, 3] |
16
|
$C_{30}$ |
[30, 4] |
20
|
$C_{32}$ |
[32, 1] |
16
|
$D_{16}$ |
[32, 18] |
8
|
$\SD_{32}$ |
[32, 19] |
4
|
$C_{35}$ |
[35, 1] |
24
|
$C_{36}$ |
[36, 2] |
24
|
$C_2^2:C_9$ |
[36, 3] |
6
|
$D_{18}$ |
[36, 4] |
6
|
$C_{39}$ |
[39, 2] |
24
|
$C_5:C_8$ |
[40, 1] |
4
|
$C_5:C_8$ |
[40, 3] |
2
|
$D_{20}$ |
[40, 6] |
4
|
$C_5:D_4$ |
[40, 8] |
4
|
$C_5\times D_4$ |
[40, 10] |
4
|
$F_7$ |
[42, 1] |
1
|
$C_7:C_6$ |
[42, 2] |
2
|
$S_3\times C_7$ |
[42, 3] |
3
|
$C_3\times D_7$ |
[42, 4] |
3
|
$D_{21}$ |
[42, 5] |
6
|
$D_{22}$ |
[44, 3] |
120
|
$C_{48}$ |
[48, 2] |
8
|
$D_{24}$ |
[48, 7] |
4
|
$C_3:Q_{16}$ |
[48, 8] |
4
|
$C_3:\SD_{16}$ |
[48, 16] |
4
|
$C_2.S_4$ |
[48, 28] |
2
|
$C_{50}$ |
[50, 2] |
20
|
$C_{13}:C_4$ |
[52, 1] |
6
|
$C_{13}:C_4$ |
[52, 3] |
3
|
$D_{26}$ |
[52, 4] |
6
|
$C_2\times C_{26}$ |
[52, 5] |
36
|
$C_{11}:C_5$ |
[55, 1] |
8
|
$C_7\times D_4$ |
[56, 9] |
12
|
$C_5\times A_4$ |
[60, 9] |
4
|
$S_3\times C_{10}$ |
[60, 11] |
8
|
$C_5:D_8$ |
[80, 15] |
8
|
$S_3\times D_7$ |
[84, 8] |
3
|
$C_7:A_4$ |
[84, 11] |
6
|
$C_{48}:C_2$ |
[96, 7] |
8
|
$C_{13}:D_4$ |
[104, 8] |
12
|
$F_{11}$ |
[110, 1] |
4
|
$C_5:S_4$ |
[120, 38] |
4
|