Distribution of groups in curves of genus 15 with quotient genus 0
| Isomorphism class | GAP/Magma Group | Distinct generating vectors |
|---|---|---|
| $C_2$ | [2, 1] | 1 |
| $C_3$ | [3, 1] | 6 |
| $C_4$ | [4, 1] | 27 |
| $C_2^2$ | [4, 2] | 52 |
| $S_3$ | [6, 1] | 65457 |
| $C_6$ | [6, 2] | 67 |
| $C_7$ | [7, 1] | 114 |
| $C_8$ | [8, 1] | 73 |
| $C_2\times C_4$ | [8, 2] | 399 |
| $D_4$ | [8, 3] | 1598 |
| $Q_8$ | [8, 4] | 62 |
| $C_2^3$ | [8, 5] | 1393 |
| $C_9$ | [9, 1] | 78 |
| $D_5$ | [10, 1] | 31250 |
| $C_{10}$ | [10, 2] | 58 |
| $C_{11}$ | [11, 1] | 182 |
| $C_3:C_4$ | [12, 1] | 111 |
| $C_{12}$ | [12, 2] | 103 |
| $A_4$ | [12, 3] | 627 |
| $D_6$ | [12, 4] | 883 |
| $C_2\times C_6$ | [12, 5] | 160 |
| $D_7$ | [14, 1] | 58824 |
| $C_{14}$ | [14, 2] | 48 |
| $C_{15}$ | [15, 1] | 28 |
| $C_{16}$ | [16, 1] | 64 |
| $C_4^2$ | [16, 2] | 400 |
| $C_4:C_4$ | [16, 4] | 136 |
| $C_2\times C_8$ | [16, 5] | 164 |
| $\OD_{16}$ | [16, 6] | 60 |
| $D_8$ | [16, 7] | 828 |
| $\SD_{16}$ | [16, 8] | 124 |
| $Q_{16}$ | [16, 9] | 28 |
| $C_2\times D_4$ | [16, 11] | 936 |
| $C_2\times Q_8$ | [16, 12] | 84 |
| $D_4:C_2$ | [16, 13] | 336 |
| $D_9$ | [18, 1] | 486 |
| $C_{18}$ | [18, 2] | 39 |
| $C_5:C_4$ | [20, 1] | 4 |
| $C_{20}$ | [20, 2] | 40 |
| $D_{10}$ | [20, 4] | 154 |
| $C_7:C_3$ | [21, 1] | 228 |
| $C_{21}$ | [21, 2] | 36 |
| $C_{22}$ | [22, 2] | 50 |
| $C_3:C_8$ | [24, 1] | 12 |
| $C_{24}$ | [24, 2] | 24 |
| $\SL(2,3)$ | [24, 3] | 14 |
| $C_3:Q_8$ | [24, 4] | 8 |
| $C_4\times S_3$ | [24, 5] | 132 |
| $D_{12}$ | [24, 6] | 52 |
| $C_6:C_4$ | [24, 7] | 36 |
| $C_3:D_4$ | [24, 8] | 64 |
| $C_2\times C_{12}$ | [24, 9] | 76 |
| $C_3\times D_4$ | [24, 10] | 28 |
| $S_4$ | [24, 12] | 180 |
| $C_2\times A_4$ | [24, 13] | 54 |
| $C_2\times D_6$ | [24, 14] | 196 |
| $C_2^2\times C_6$ | [24, 15] | 364 |
| $C_7:C_4$ | [28, 1] | 78 |
| $D_{14}$ | [28, 3] | 2472 |
| $C_3\times D_5$ | [30, 2] | 4 |
| $D_{15}$ | [30, 3] | 900 |
| $C_{30}$ | [30, 4] | 12 |
| $C_{31}$ | [31, 1] | 160 |
| $C_{32}$ | [32, 1] | 72 |
| $D_4:C_4$ | [32, 9] | 32 |
| $Q_8:C_4$ | [32, 10] | 24 |
| $C_4\wr C_2$ | [32, 11] | 28 |
| $C_8:C_4$ | [32, 13] | 24 |
| $C_8:C_4$ | [32, 14] | 24 |
| $C_2\times C_{16}$ | [32, 16] | 40 |
| $\OD_{32}$ | [32, 17] | 12 |
| $D_{16}$ | [32, 18] | 168 |
| $\SD_{32}$ | [32, 19] | 20 |
| $C_2\times D_8$ | [32, 39] | 296 |
| $C_2\times \SD_{16}$ | [32, 40] | 16 |
| $C_2\times Q_{16}$ | [32, 41] | 16 |
| $D_8:C_2$ | [32, 42] | 24 |
| $D_8:C_2$ | [32, 43] | 48 |
| $Q_{16}:C_2$ | [32, 44] | 8 |
| $C_{33}$ | [33, 1] | 90 |
| $C_{35}$ | [35, 1] | 60 |
| $C_{36}$ | [36, 2] | 36 |
| $C_2^2:C_9$ | [36, 3] | 9 |
| $D_{18}$ | [36, 4] | 12 |
| $C_5:C_8$ | [40, 1] | 12 |
| $C_{40}$ | [40, 2] | 16 |
| $C_4\times D_5$ | [40, 5] | 20 |
| $D_{20}$ | [40, 6] | 16 |
| $F_7$ | [42, 1] | 24 |
| $C_7:C_6$ | [42, 2] | 4 |
| $C_3\times D_7$ | [42, 4] | 24 |
| $D_{21}$ | [42, 5] | 432 |
| $C_{42}$ | [42, 6] | 12 |
| $C_{44}$ | [44, 2] | 20 |
| $C_{45}$ | [45, 1] | 24 |
| $C_{48}$ | [48, 2] | 16 |
| $C_4^2:C_3$ | [48, 3] | 12 |
| $S_3\times C_8$ | [48, 4] | 8 |
| $C_{24}:C_2$ | [48, 5] | 4 |
| $C_6:C_8$ | [48, 9] | 8 |
| $C_3:\OD_{16}$ | [48, 10] | 4 |
| $C_4\times C_{12}$ | [48, 20] | 96 |
| $C_4:C_{12}$ | [48, 22] | 24 |
| $C_2.S_4$ | [48, 28] | 2 |
| $\GL(2,3)$ | [48, 29] | 13 |
| $C_2\times \SL(2,3)$ | [48, 32] | 2 |
| $\SL(2,3):C_2$ | [48, 33] | 10 |
| $C_2\times D_{12}$ | [48, 36] | 16 |
| $D_{12}:C_2$ | [48, 37] | 4 |
| $S_3\times D_4$ | [48, 38] | 8 |
| $D_4:S_3$ | [48, 39] | 4 |
| $C_6:D_4$ | [48, 43] | 32 |
| $C_2\times S_4$ | [48, 48] | 14 |
| $C_7^2$ | [49, 2] | 336 |
| $C_{11}:C_5$ | [55, 1] | 4 |
| $C_4\times D_7$ | [56, 4] | 96 |
| $D_{28}$ | [56, 5] | 96 |
| $C_7:D_4$ | [56, 7] | 96 |
| $C_2\times D_{14}$ | [56, 12] | 288 |
| $C_{15}:C_4$ | [60, 3] | 8 |
| $C_{60}$ | [60, 4] | 8 |
| $A_5$ | [60, 5] | 30 |
| $D_{30}$ | [60, 12] | 8 |
| $C_{62}$ | [62, 2] | 30 |
| $Q_{16}:C_4$ | [64, 39] | 16 |
| $D_8:C_4$ | [64, 41] | 4 |
| $C_{16}:C_4$ | [64, 47] | 16 |
| $C_{16}:C_4$ | [64, 48] | 16 |
| $C_2\times C_{32}$ | [64, 50] | 32 |
| $\OD_{64}$ | [64, 51] | 8 |
| $C_2\times D_{16}$ | [64, 186] | 32 |
| $D_{16}:C_2$ | [64, 189] | 8 |
| $D_{16}:C_2$ | [64, 190] | 8 |
| $S_3\times C_{11}$ | [66, 1] | 10 |
| $C_7\times D_5$ | [70, 1] | 12 |
| $C_2^2:D_9$ | [72, 15] | 12 |
| $C_2^2:C_{18}$ | [72, 16] | 3 |
| $C_8\times D_5$ | [80, 4] | 16 |
| $C_{40}:C_2$ | [80, 5] | 8 |
| $C_7:C_{12}$ | [84, 1] | 4 |
| $S_3\times D_7$ | [84, 8] | 24 |
| $C_{31}:C_3$ | [93, 1] | 10 |
| $D_{12}:C_4$ | [96, 12] | 8 |
| $D_{12}:C_4$ | [96, 16] | 16 |
| $C_4^2:S_3$ | [96, 64] | 2 |
| $\SL(2,3):C_4$ | [96, 66] | 4 |
| $\GU(2,3)$ | [96, 67] | 4 |
| $\GL(2,3):C_2$ | [96, 192] | 4 |
| $\GL(2,3):C_2$ | [96, 193] | 4 |
| $C_7\times D_7$ | [98, 3] | 18 |
| $D_4\times D_7$ | [112, 31] | 48 |
| $D_{28}:C_2$ | [112, 34] | 48 |
| $\SL(2,5)$ | [120, 5] | 2 |
| $C_4\times D_{15}$ | [120, 27] | 16 |
| $C_2\times A_5$ | [120, 35] | 2 |
| $D_{16}:C_4$ | [128, 147] | 32 |
| $D_{16}:C_4$ | [128, 150] | 8 |
| $C_2^2:D_{18}$ | [144, 109] | 6 |
| $C_7^2:C_3$ | [147, 5] | 12 |
| $C_7:\SL(2,3)$ | [168, 23] | 12 |
| $\GL(3,2)$ | [168, 42] | 2 |
| $F_8:C_3$ | [168, 43] | 4 |
| $\SL(2,5):C_2$ | [240, 93] | 4 |
| $C_7^2:S_3$ | [294, 7] | 6 |
| $Q_8.F_7$ | [336, 134] | 12 |
| $\PGL(2,7)$ | [336, 208] | 1 |
| $\SL(2,8)$ | [504, 156] | 3 |