Distribution of groups in curves of genus 10 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] | 10 |
| $C_2^2$ | [4, 2] | 21 |
| $C_5$ | [5, 1] | 24 |
| $S_3$ | [6, 1] | 3636 |
| $C_6$ | [6, 2] | 35 |
| $C_8$ | [8, 1] | 24 |
| $D_4$ | [8, 3] | 93 |
| $Q_8$ | [8, 4] | 13 |
| $C_9$ | [9, 1] | 20 |
| $C_3^2$ | [9, 2] | 184 |
| $D_5$ | [10, 1] | 1250 |
| $C_{10}$ | [10, 2] | 18 |
| $C_{11}$ | [11, 1] | 65 |
| $C_3:C_4$ | [12, 1] | 14 |
| $C_{12}$ | [12, 2] | 26 |
| $A_4$ | [12, 3] | 72 |
| $D_6$ | [12, 4] | 174 |
| $C_2\times C_6$ | [12, 5] | 56 |
| $C_{14}$ | [14, 2] | 14 |
| $C_{15}$ | [15, 1] | 24 |
| $C_{16}$ | [16, 1] | 8 |
| $D_8$ | [16, 7] | 4 |
| $\SD_{16}$ | [16, 8] | 34 |
| $Q_{16}$ | [16, 9] | 4 |
| $D_9$ | [18, 1] | 3240 |
| $C_{18}$ | [18, 2] | 12 |
| $C_3\times S_3$ | [18, 3] | 75 |
| $C_3:S_3$ | [18, 4] | 3184 |
| $C_3\times C_6$ | [18, 5] | 148 |
| $C_5:C_4$ | [20, 1] | 2 |
| $C_{20}$ | [20, 2] | 4 |
| $D_{10}$ | [20, 4] | 102 |
| $C_7:C_3$ | [21, 1] | 28 |
| $C_{21}$ | [21, 2] | 16 |
| $D_{11}$ | [22, 1] | 30 |
| $C_{22}$ | [22, 2] | 55 |
| $C_{24}$ | [24, 2] | 20 |
| $\SL(2,3)$ | [24, 3] | 10 |
| $D_{12}$ | [24, 6] | 68 |
| $C_3:D_4$ | [24, 8] | 36 |
| $C_3\times D_4$ | [24, 10] | 10 |
| $C_3\times Q_8$ | [24, 11] | 2 |
| $S_4$ | [24, 12] | 16 |
| $C_{25}$ | [25, 1] | 40 |
| $C_3\times C_9$ | [27, 2] | 18 |
| $\He_3$ | [27, 3] | 106 |
| $C_9:C_3$ | [27, 4] | 2 |
| $C_3^3$ | [27, 5] | 468 |
| $C_{28}$ | [28, 2] | 12 |
| $C_3\times D_5$ | [30, 2] | 8 |
| $D_{15}$ | [30, 3] | 8 |
| $C_{30}$ | [30, 4] | 12 |
| $C_{33}$ | [33, 1] | 20 |
| $D_{18}$ | [36, 4] | 72 |
| $C_3:C_{12}$ | [36, 6] | 8 |
| $C_3\times C_{12}$ | [36, 8] | 48 |
| $C_3^2:C_4$ | [36, 9] | 20 |
| $S_3^2$ | [36, 10] | 22 |
| $C_3\times A_4$ | [36, 11] | 14 |
| $C_6\times S_3$ | [36, 12] | 16 |
| $C_6:S_3$ | [36, 13] | 72 |
| $C_6^2$ | [36, 14] | 48 |
| $C_{40}$ | [40, 2] | 8 |
| $C_5:Q_8$ | [40, 4] | 4 |
| $D_{20}$ | [40, 6] | 4 |
| $C_7:C_6$ | [42, 2] | 4 |
| $C_{42}$ | [42, 6] | 12 |
| $C_{11}:C_4$ | [44, 1] | 5 |
| $D_{22}$ | [44, 3] | 5 |
| $C_2\times C_{22}$ | [44, 4] | 30 |
| $C_3\times \SD_{16}$ | [48, 26] | 4 |
| $\GL(2,3)$ | [48, 29] | 32 |
| $S_3\times C_9$ | [54, 4] | 6 |
| $C_3^2:C_6$ | [54, 5] | 15 |
| $C_3^2:S_3$ | [54, 8] | 60 |
| $C_2\times \He_3$ | [54, 10] | 24 |
| $S_3\times C_3^2$ | [54, 12] | 24 |
| $C_3^2:C_6$ | [54, 13] | 24 |
| $A_5$ | [60, 5] | 20 |
| $C_3\times D_{10}$ | [60, 10] | 8 |
| $C_{21}:C_3$ | [63, 3] | 12 |
| $C_2^2:D_9$ | [72, 15] | 36 |
| $C_3:D_{12}$ | [72, 23] | 4 |
| $C_3\times \SL(2,3)$ | [72, 25] | 6 |
| $C_3\times D_{12}$ | [72, 28] | 8 |
| $C_6\wr C_2$ | [72, 30] | 4 |
| $F_9$ | [72, 39] | 2 |
| $\SOPlus(4,2)$ | [72, 40] | 4 |
| $\PSU(3,2)$ | [72, 41] | 4 |
| $C_3\times S_4$ | [72, 42] | 2 |
| $C_3:S_4$ | [72, 43] | 24 |
| $C_{40}:C_2$ | [80, 6] | 8 |
| $C_3\wr C_3$ | [81, 7] | 12 |
| $\He_3:C_3$ | [81, 9] | 18 |
| $C_{11}:D_4$ | [88, 7] | 10 |
| $\He_3:C_4$ | [108, 15] | 6 |
| $C_3^2:D_6$ | [108, 17] | 4 |
| $C_3^2:A_4$ | [108, 22] | 18 |
| $C_3^2:D_6$ | [108, 25] | 4 |
| $C_3^3:C_4$ | [108, 37] | 4 |
| $C_3\times S_3^2$ | [108, 38] | 2 |
| $C_3:S_3^2$ | [108, 40] | 2 |
| $C_3\times \GL(2,3)$ | [144, 122] | 4 |
| $F_9:C_2$ | [144, 182] | 2 |
| $\He_3.C_6$ | [162, 14] | 6 |
| $\PSL(2,7)$ | [168, 42] | 2 |
| $\GL(2,4)$ | [180, 19] | 4 |
| $\He_3:D_4$ | [216, 87] | 2 |
| $C_3^2:S_4$ | [216, 92] | 2 |
| $\PU(3,2)$ | [216, 153] | 4 |
| $S_3^2:S_3$ | [216, 158] | 2 |
| $C_3^3:A_4$ | [324, 160] | 4 |
| $A_6$ | [360, 118] | 4 |
| $C_3^2:\GL(2,3)$ | [432, 734] | 2 |