Distribution of groups in curves of genus 7

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