Distribution of groups in curves of genus 9 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] | 25 |
| $S_3$ | [6, 1] | 801 |
| $C_6$ | [6, 2] | 21 |
| $C_7$ | [7, 1] | 36 |
| $C_8$ | [8, 1] | 28 |
| $C_2\times C_4$ | [8, 2] | 101 |
| $D_4$ | [8, 3] | 158 |
| $Q_8$ | [8, 4] | 6 |
| $C_2^3$ | [8, 5] | 315 |
| $C_9$ | [9, 1] | 12 |
| $D_5$ | [10, 1] | 150 |
| $C_{10}$ | [10, 2] | 17 |
| $C_3:C_4$ | [12, 1] | 6 |
| $C_{12}$ | [12, 2] | 26 |
| $A_4$ | [12, 3] | 69 |
| $D_6$ | [12, 4] | 59 |
| $C_2\times C_6$ | [12, 5] | 30 |
| $C_{14}$ | [14, 2] | 18 |
| $C_{15}$ | [15, 1] | 8 |
| $C_4^2$ | [16, 2] | 72 |
| $C_2^2:C_4$ | [16, 3] | 122 |
| $C_4:C_4$ | [16, 4] | 26 |
| $C_2\times C_8$ | [16, 5] | 48 |
| $\OD_{16}$ | [16, 6] | 14 |
| $D_8$ | [16, 7] | 264 |
| $\SD_{16}$ | [16, 8] | 8 |
| $Q_{16}$ | [16, 9] | 8 |
| $C_2^2\times C_4$ | [16, 10] | 248 |
| $C_2\times D_4$ | [16, 11] | 148 |
| $C_2\times Q_8$ | [16, 12] | 6 |
| $D_4:C_2$ | [16, 13] | 38 |
| $C_2^4$ | [16, 14] | 1120 |
| $D_9$ | [18, 1] | 243 |
| $C_{18}$ | [18, 2] | 3 |
| $C_{19}$ | [19, 1] | 60 |
| $C_5:C_4$ | [20, 1] | 4 |
| $C_{20}$ | [20, 2] | 16 |
| $F_5$ | [20, 3] | 10 |
| $D_{10}$ | [20, 4] | 66 |
| $C_2\times C_{10}$ | [20, 5] | 24 |
| $C_{21}$ | [21, 2] | 30 |
| $C_3:C_8$ | [24, 1] | 6 |
| $C_{24}$ | [24, 2] | 16 |
| $\SL(2,3)$ | [24, 3] | 3 |
| $C_4\times S_3$ | [24, 5] | 14 |
| $D_{12}$ | [24, 6] | 44 |
| $C_6:C_4$ | [24, 7] | 4 |
| $C_3:D_4$ | [24, 8] | 10 |
| $C_2\times C_{12}$ | [24, 9] | 8 |
| $C_3\times D_4$ | [24, 10] | 8 |
| $S_4$ | [24, 12] | 39 |
| $C_2\times A_4$ | [24, 13] | 17 |
| $C_2\times D_6$ | [24, 14] | 27 |
| $C_2^2\times C_6$ | [24, 15] | 84 |
| $C_{27}$ | [27, 1] | 18 |
| $C_{28}$ | [28, 2] | 12 |
| $C_{30}$ | [30, 4] | 8 |
| $C_4\times C_8$ | [32, 3] | 64 |
| $C_8:C_4$ | [32, 4] | 16 |
| $C_2^2:C_8$ | [32, 5] | 8 |
| $C_2^3:C_4$ | [32, 6] | 22 |
| $C_4.D_4$ | [32, 8] | 4 |
| $D_4:C_4$ | [32, 9] | 32 |
| $C_4\wr C_2$ | [32, 11] | 8 |
| $C_4:C_8$ | [32, 12] | 16 |
| $D_{16}$ | [32, 18] | 32 |
| $\SD_{32}$ | [32, 19] | 32 |
| $C_2^3:C_4$ | [32, 22] | 96 |
| $C_4\times D_4$ | [32, 25] | 32 |
| $C_2^2\wr C_2$ | [32, 27] | 56 |
| $C_4:D_4$ | [32, 28] | 24 |
| $C_2^2.D_4$ | [32, 30] | 16 |
| $C_4^2:C_2$ | [32, 31] | 16 |
| $C_4:D_4$ | [32, 34] | 72 |
| $C_2\times D_8$ | [32, 39] | 72 |
| $C_2\times \SD_{16}$ | [32, 40] | 8 |
| $D_8:C_2$ | [32, 42] | 8 |
| $D_8:C_2$ | [32, 43] | 8 |
| $C_2^2\times D_4$ | [32, 46] | 96 |
| $D_4:C_2^2$ | [32, 49] | 9 |
| $C_4.C_2^3$ | [32, 50] | 1 |
| $C_9:C_4$ | [36, 1] | 6 |
| $C_{36}$ | [36, 2] | 6 |
| $D_{18}$ | [36, 4] | 6 |
| $C_{38}$ | [38, 2] | 18 |
| $C_{10}:C_4$ | [40, 7] | 8 |
| $C_5:D_4$ | [40, 8] | 8 |
| $C_2\times C_{20}$ | [40, 9] | 16 |
| $C_2\times F_5$ | [40, 12] | 2 |
| $C_2\times D_{10}$ | [40, 13] | 24 |
| $S_3\times C_7$ | [42, 3] | 6 |
| $S_3\times C_8$ | [48, 4] | 8 |
| $C_{24}:C_2$ | [48, 5] | 4 |
| $C_3:D_8$ | [48, 15] | 16 |
| $C_6.D_4$ | [48, 19] | 8 |
| $C_2^2:C_{12}$ | [48, 21] | 8 |
| $\GL(2,3)$ | [48, 29] | 12 |
| $A_4:C_4$ | [48, 30] | 4 |
| $C_4\times A_4$ | [48, 31] | 8 |
| $C_2\times \SL(2,3)$ | [48, 32] | 2 |
| $\SL(2,3):C_2$ | [48, 33] | 6 |
| $S_3\times D_4$ | [48, 38] | 4 |
| $C_6:D_4$ | [48, 43] | 8 |
| $C_2\times S_4$ | [48, 48] | 10 |
| $C_2^2:A_4$ | [48, 50] | 30 |
| $C_{19}:C_3$ | [57, 1] | 6 |
| $A_5$ | [60, 5] | 3 |
| $C_2^3:C_8$ | [64, 4] | 8 |
| $D_4:C_8$ | [64, 6] | 16 |
| $C_4^2.C_2^2$ | [64, 10] | 8 |
| $C_4.D_8$ | [64, 12] | 16 |
| $C_2^2.C_4^2$ | [64, 23] | 16 |
| $C_4^2:C_4$ | [64, 34] | 4 |
| $C_4^2:C_4$ | [64, 35] | 8 |
| $C_4^2.C_4$ | [64, 36] | 4 |
| $C_2^3:D_4$ | [64, 73] | 64 |
| $D_4:D_4$ | [64, 128] | 32 |
| $D_4:D_4$ | [64, 134] | 4 |
| $D_4.D_4$ | [64, 135] | 4 |
| $C_2\wr C_2^2$ | [64, 138] | 12 |
| $C_4:D_8$ | [64, 140] | 32 |
| $C_8:D_4$ | [64, 177] | 32 |
| $D_{16}:C_2$ | [64, 190] | 16 |
| $C_4\times D_9$ | [72, 5] | 12 |
| $D_{10}:C_4$ | [80, 14] | 16 |
| $C_2^3.A_4$ | [96, 3] | 8 |
| $C_2^2.D_{12}$ | [96, 13] | 4 |
| $\GU(2,3)$ | [96, 67] | 2 |
| $C_2^3:A_4$ | [96, 70] | 2 |
| $C_4\times S_4$ | [96, 186] | 4 |
| $C_4:S_4$ | [96, 187] | 4 |
| $\GL(2,3):C_2$ | [96, 193] | 6 |
| $D_4.A_4$ | [96, 202] | 2 |
| $C_2^2:S_4$ | [96, 227] | 9 |
| $S_5$ | [120, 34] | 1 |
| $C_2\times A_5$ | [120, 35] | 2 |
| $C_2^3.D_8$ | [128, 75] | 16 |
| $C_4^2.D_4$ | [128, 134] | 4 |
| $C_4^2.D_4$ | [128, 136] | 4 |
| $C_4^2.(C_2\times C_4)$ | [128, 138] | 8 |
| $C_2.C_2^4:C_5$ | [160, 199] | 2 |
| $C_2^3.(C_2\times A_4)$ | [192, 194] | 8 |
| $C_2^3:S_4$ | [192, 955] | 2 |
| $D_4.S_4$ | [192, 990] | 4 |
| $C_2.C_2^4:D_5$ | [320, 1582] | 4 |