Distribution of groups in curves of genus 14 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] | 36 |
| $C_5$ | [5, 1] | 44 |
| $S_3$ | [6, 1] | 14546 |
| $C_6$ | [6, 2] | 59 |
| $C_8$ | [8, 1] | 54 |
| $D_4$ | [8, 3] | 557 |
| $Q_8$ | [8, 4] | 109 |
| $C_9$ | [9, 1] | 36 |
| $D_5$ | [10, 1] | 3750 |
| $C_{10}$ | [10, 2] | 45 |
| $C_3:C_4$ | [12, 1] | 33 |
| $C_{12}$ | [12, 2] | 54 |
| $A_4$ | [12, 3] | 144 |
| $D_6$ | [12, 4] | 392 |
| $C_2\times C_6$ | [12, 5] | 148 |
| $D_7$ | [14, 1] | 7203 |
| $C_{14}$ | [14, 2] | 3 |
| $C_{15}$ | [15, 1] | 32 |
| $C_{16}$ | [16, 1] | 48 |
| $D_8$ | [16, 7] | 148 |
| $\SD_{16}$ | [16, 8] | 74 |
| $Q_{16}$ | [16, 9] | 4 |
| $D_9$ | [18, 1] | 24 |
| $C_{18}$ | [18, 2] | 39 |
| $C_5:C_4$ | [20, 1] | 8 |
| $C_{20}$ | [20, 2] | 30 |
| $F_5$ | [20, 3] | 25 |
| $D_{10}$ | [20, 4] | 108 |
| $C_2\times C_{10}$ | [20, 5] | 42 |
| $C_{21}$ | [21, 2] | 12 |
| $C_3:C_8$ | [24, 1] | 6 |
| $C_{24}$ | [24, 2] | 6 |
| $\SL(2,3)$ | [24, 3] | 9 |
| $C_3:Q_8$ | [24, 4] | 6 |
| $D_{12}$ | [24, 6] | 10 |
| $C_3:D_4$ | [24, 8] | 88 |
| $C_3\times D_4$ | [24, 10] | 11 |
| $C_3\times Q_8$ | [24, 11] | 12 |
| $S_4$ | [24, 12] | 24 |
| $D_{13}$ | [26, 1] | 14280 |
| $C_7:C_4$ | [28, 1] | 3 |
| $C_{28}$ | [28, 2] | 6 |
| $D_{14}$ | [28, 3] | 297 |
| $C_{29}$ | [29, 1] | 140 |
| $C_5\times S_3$ | [30, 1] | 8 |
| $C_3\times D_5$ | [30, 2] | 8 |
| $D_{15}$ | [30, 3] | 20 |
| $C_{30}$ | [30, 4] | 20 |
| $C_{32}$ | [32, 1] | 32 |
| $D_{16}$ | [32, 18] | 16 |
| $C_{35}$ | [35, 1] | 36 |
| $D_{18}$ | [36, 4] | 6 |
| $C_2\times C_{18}$ | [36, 5] | 36 |
| $C_{13}:C_3$ | [39, 1] | 56 |
| $C_5:C_8$ | [40, 1] | 4 |
| $C_{40}$ | [40, 2] | 16 |
| $C_5:C_8$ | [40, 3] | 2 |
| $D_{20}$ | [40, 6] | 4 |
| $C_5:D_4$ | [40, 8] | 8 |
| $C_5\times Q_8$ | [40, 11] | 12 |
| $C_3\times D_7$ | [42, 4] | 12 |
| $D_{21}$ | [42, 5] | 12 |
| $C_{42}$ | [42, 6] | 6 |
| $C_3:C_{16}$ | [48, 1] | 4 |
| $D_{24}$ | [48, 7] | 4 |
| $C_3:D_8$ | [48, 15] | 4 |
| $C_3:Q_{16}$ | [48, 18] | 4 |
| $C_3\times D_8$ | [48, 25] | 4 |
| $C_3\times \SD_{16}$ | [48, 26] | 4 |
| $\GL(2,3)$ | [48, 29] | 2 |
| $C_{13}:C_4$ | [52, 3] | 42 |
| $D_{26}$ | [52, 4] | 168 |
| $C_{56}$ | [56, 2] | 12 |
| $C_7:Q_8$ | [56, 3] | 6 |
| $D_{28}$ | [56, 5] | 6 |
| $C_{58}$ | [58, 2] | 28 |
| $C_{15}:C_4$ | [60, 3] | 4 |
| $C_{15}:C_4$ | [60, 7] | 2 |
| $S_3\times D_5$ | [60, 8] | 2 |
| $D_{30}$ | [60, 12] | 4 |
| $C_2\times C_{30}$ | [60, 13] | 24 |
| $C_5\times D_7$ | [70, 2] | 12 |
| $C_{13}:C_6$ | [78, 1] | 32 |
| $C_{13}:C_6$ | [78, 2] | 8 |
| $Q_8:D_5$ | [80, 17] | 8 |
| $C_3\times D_{14}$ | [84, 12] | 12 |
| $C_3:D_{16}$ | [96, 33] | 8 |
| $C_{56}:C_2$ | [112, 5] | 12 |
| $\SL(2,5)$ | [120, 5] | 2 |
| $C_{15}:D_4$ | [120, 30] | 8 |
| $C_{26}:C_6$ | [156, 8] | 8 |
| $\PSL(2,13)$ | [1092, 25] | 6 |