Distribution of groups in curves of genus 7 with quotient genus 0
| Isomorphism class | GAP/Magma Group | Distinct generating vectors | Topologically inequivalent actions | Braid inequivalent actions |
|---|---|---|---|---|
| $C_2$ | [2, 1] | 1 | 1 | 1 |
| $C_3$ | [3, 1] | 4 | 2 | 4 |
| $C_4$ | [4, 1] | 9 | 5 | 9 |
| $C_2^2$ | [4, 2] | 18 | 4 | 18 |
| $S_3$ | [6, 1] | 400 | 2 | 2 |
| $C_6$ | [6, 2] | 17 | 9 | 17 |
| $C_8$ | [8, 1] | 15 | 6 | 15 |
| $C_2\times C_4$ | [8, 2] | 54 | 11 | 54 |
| $D_4$ | [8, 3] | 46 | 5 | 8 |
| $Q_8$ | [8, 4] | 6 | 1 | 3 |
| $C_2^3$ | [8, 5] | 155 | 4 | 155 |
| $C_9$ | [9, 1] | 14 | 3 | 14 |
| $C_3^2$ | [9, 2] | 80 | 4 | 80 |
| $C_{10}$ | [10, 2] | 8 | 2 | 8 |
| $C_3:C_4$ | [12, 1] | 16 | 3 | 5 |
| $C_{12}$ | [12, 2] | 16 | 4 | 16 |
| $A_4$ | [12, 3] | 24 | 1 | 2 |
| $D_6$ | [12, 4] | 96 | 4 | 7 |
| $C_2\times C_6$ | [12, 5] | 24 | 2 | 24 |
| $D_7$ | [14, 1] | 147 | 1 | 3 |
| $C_{14}$ | [14, 2] | 3 | 1 | 3 |
| $C_{15}$ | [15, 1] | 8 | 1 | 8 |
| $C_{16}$ | [16, 1] | 20 | 3 | 20 |
| $C_4^2$ | [16, 2] | 48 | 1 | 48 |
| $C_4:C_4$ | [16, 4] | 12 | 3 | 12 |
| $C_2\times C_8$ | [16, 5] | 20 | 3 | 20 |
| $\OD_{16}$ | [16, 6] | 6 | 2 | 4 |
| $D_8$ | [16, 7] | 28 | 3 | 7 |
| $\SD_{16}$ | [16, 8] | 6 | 2 | 3 |
| $C_2\times D_4$ | [16, 11] | 52 | 4 | 28 |
| $C_2\times Q_8$ | [16, 12] | 8 | 1 | 8 |
| $D_4:C_2$ | [16, 13] | 20 | 3 | 11 |
| $D_9$ | [18, 1] | 72 | 1 | 1 |
| $C_{18}$ | [18, 2] | 12 | 2 | 12 |
| $C_3\times S_3$ | [18, 3] | 16 | 5 | 9 |
| $C_3:S_3$ | [18, 4] | 288 | 1 | 4 |
| $C_3\times C_6$ | [18, 5] | 24 | 1 | 24 |
| $C_{20}$ | [20, 2] | 8 | 1 | 8 |
| $C_{21}$ | [21, 2] | 6 | 1 | 6 |
| $C_{24}$ | [24, 2] | 8 | 1 | 8 |
| $\SL(2,3)$ | [24, 3] | 4 | 2 | 4 |
| $C_4\times S_3$ | [24, 5] | 16 | 2 | 4 |
| $D_{12}$ | [24, 6] | 16 | 1 | 1 |
| $C_3:D_4$ | [24, 8] | 16 | 1 | 1 |
| $C_2\times C_{12}$ | [24, 9] | 16 | 1 | 16 |
| $S_4$ | [24, 12] | 16 | 2 | 2 |
| $C_2\times A_4$ | [24, 13] | 8 | 2 | 4 |
| $C_2\times D_6$ | [24, 14] | 48 | 1 | 12 |
| $C_3\times C_9$ | [27, 2] | 54 | 1 | 54 |
| $C_9:C_3$ | [27, 4] | 6 | 2 | 6 |
| $C_7:C_4$ | [28, 1] | 6 | 1 | 6 |
| $C_{28}$ | [28, 2] | 6 | 1 | 6 |
| $D_{14}$ | [28, 3] | 6 | 1 | 6 |
| $C_{30}$ | [30, 4] | 8 | 1 | 8 |
| $Q_8:C_4$ | [32, 10] | 8 | 1 | 8 |
| $C_4\wr C_2$ | [32, 11] | 4 | 1 | 4 |
| $C_8:C_4$ | [32, 13] | 8 | 1 | 8 |
| $C_8:C_4$ | [32, 14] | 8 | 1 | 8 |
| $C_2\times C_{16}$ | [32, 16] | 16 | 1 | 16 |
| $\OD_{32}$ | [32, 17] | 4 | 1 | 4 |
| $C_2\times D_8$ | [32, 39] | 16 | 1 | 16 |
| $D_8:C_2$ | [32, 42] | 4 | 1 | 2 |
| $D_8:C_2$ | [32, 43] | 4 | 1 | 2 |
| $C_3:C_{12}$ | [36, 6] | 4 | 1 | 4 |
| $S_3^2$ | [36, 10] | 8 | 1 | 2 |
| $C_3\times D_7$ | [42, 4] | 6 | 1 | 6 |
| $C_2\times \SL(2,3)$ | [48, 32] | 4 | 1 | 4 |
| $\SL(2,3):C_2$ | [48, 33] | 4 | 1 | 4 |
| $S_3\times D_4$ | [48, 38] | 8 | 1 | 2 |
| $D_{12}:C_2$ | [48, 41] | 8 | 1 | 2 |
| $C_2\times S_4$ | [48, 48] | 8 | 1 | 2 |
| $C_3\times D_9$ | [54, 3] | 6 | 1 | 6 |
| $C_9:C_6$ | [54, 6] | 2 | 2 | 2 |
| $C_4\times D_7$ | [56, 4] | 12 | 1 | 12 |
| $F_8$ | [56, 11] | 3 | 1 | 3 |
| $D_8:C_4$ | [64, 38] | 16 | 1 | 16 |
| $D_8:C_4$ | [64, 41] | 4 | 1 | 4 |
| $C_3\times \SL(2,3)$ | [72, 25] | 6 | 1 | 6 |
| $\SL(2,3):S_3$ | [144, 127] | 4 | 1 | 4 |
| $\SL(2,8)$ | [504, 156] | 3 | 1 | 3 |