Distribution of groups in curves of genus 12 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] | 28 |
| $C_5$ | [5, 1] | 33 |
| $S_3$ | [6, 1] | 7273 |
| $C_6$ | [6, 2] | 40 |
| $C_7$ | [7, 1] | 66 |
| $C_8$ | [8, 1] | 34 |
| $D_4$ | [8, 3] | 365 |
| $Q_8$ | [8, 4] | 13 |
| $C_9$ | [9, 1] | 45 |
| $D_5$ | [10, 1] | 40 |
| $C_{10}$ | [10, 2] | 55 |
| $C_3:C_4$ | [12, 1] | 25 |
| $C_{12}$ | [12, 2] | 47 |
| $A_4$ | [12, 3] | 209 |
| $D_6$ | [12, 4] | 312 |
| $C_2\times C_6$ | [12, 5] | 65 |
| $C_{13}$ | [13, 1] | 105 |
| $D_7$ | [14, 1] | 40 |
| $C_{14}$ | [14, 2] | 71 |
| $C_{15}$ | [15, 1] | 48 |
| $C_{16}$ | [16, 1] | 16 |
| $D_8$ | [16, 7] | 74 |
| $\SD_{16}$ | [16, 8] | 4 |
| $Q_{16}$ | [16, 9] | 2 |
| $D_9$ | [18, 1] | 12 |
| $C_{18}$ | [18, 2] | 27 |
| $C_5:C_4$ | [20, 1] | 6 |
| $C_{20}$ | [20, 2] | 10 |
| $F_5$ | [20, 3] | 4 |
| $D_{10}$ | [20, 4] | 6 |
| $C_2\times C_{10}$ | [20, 5] | 38 |
| $C_7:C_3$ | [21, 1] | 9 |
| $C_{21}$ | [21, 2] | 3 |
| $D_{11}$ | [22, 1] | 7320 |
| $C_3:C_8$ | [24, 1] | 2 |
| $C_{24}$ | [24, 2] | 4 |
| $\SL(2,3)$ | [24, 3] | 9 |
| $C_3:Q_8$ | [24, 4] | 4 |
| $D_{12}$ | [24, 6] | 148 |
| $C_3:D_4$ | [24, 8] | 6 |
| $C_3\times D_4$ | [24, 10] | 10 |
| $S_4$ | [24, 12] | 45 |
| $C_{25}$ | [25, 1] | 60 |
| $D_{13}$ | [26, 1] | 42 |
| $C_{26}$ | [26, 2] | 78 |
| $C_{27}$ | [27, 1] | 54 |
| $C_{28}$ | [28, 2] | 30 |
| $D_{14}$ | [28, 3] | 18 |
| $C_2\times C_{14}$ | [28, 4] | 48 |
| $C_5\times S_3$ | [30, 1] | 12 |
| $D_{15}$ | [30, 3] | 16 |
| $C_{30}$ | [30, 4] | 20 |
| $C_{32}$ | [32, 1] | 16 |
| $D_{16}$ | [32, 18] | 8 |
| $\SD_{32}$ | [32, 19] | 4 |
| $C_{35}$ | [35, 1] | 24 |
| $C_{36}$ | [36, 2] | 24 |
| $C_2^2:C_9$ | [36, 3] | 6 |
| $D_{18}$ | [36, 4] | 6 |
| $C_{39}$ | [39, 2] | 24 |
| $C_5:C_8$ | [40, 1] | 4 |
| $C_5:C_8$ | [40, 3] | 2 |
| $D_{20}$ | [40, 6] | 4 |
| $C_5:D_4$ | [40, 8] | 4 |
| $C_5\times D_4$ | [40, 10] | 4 |
| $F_7$ | [42, 1] | 1 |
| $C_7:C_6$ | [42, 2] | 2 |
| $S_3\times C_7$ | [42, 3] | 3 |
| $C_3\times D_7$ | [42, 4] | 3 |
| $D_{21}$ | [42, 5] | 6 |
| $D_{22}$ | [44, 3] | 120 |
| $C_{48}$ | [48, 2] | 8 |
| $D_{24}$ | [48, 7] | 4 |
| $C_3:Q_{16}$ | [48, 8] | 4 |
| $C_3:\SD_{16}$ | [48, 16] | 4 |
| $C_2.S_4$ | [48, 28] | 2 |
| $C_{50}$ | [50, 2] | 20 |
| $C_{13}:C_4$ | [52, 1] | 6 |
| $C_{13}:C_4$ | [52, 3] | 3 |
| $D_{26}$ | [52, 4] | 6 |
| $C_2\times C_{26}$ | [52, 5] | 36 |
| $C_{11}:C_5$ | [55, 1] | 8 |
| $C_7\times D_4$ | [56, 9] | 12 |
| $C_5\times A_4$ | [60, 9] | 4 |
| $S_3\times C_{10}$ | [60, 11] | 8 |
| $C_5:D_8$ | [80, 15] | 8 |
| $S_3\times D_7$ | [84, 8] | 3 |
| $C_7:A_4$ | [84, 11] | 6 |
| $C_{48}:C_2$ | [96, 7] | 8 |
| $C_{13}:D_4$ | [104, 8] | 12 |
| $F_{11}$ | [110, 1] | 4 |
| $C_5:S_4$ | [120, 38] | 4 |