Distribution of groups in curves of genus 10

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 5
$C_4$ [4,1] 10
$C_2^2$ [4,2] 21
$C_5$ [5,1] 24
$S_3$ [6,1] 3636
$C_6$ [6,2] 35
$C_8$ [8,1] 24
$D_4$ [8,3] 93
$Q_8$ [8,4] 13
$C_9$ [9,1] 20
$C_3^2$ [9,2] 184
$D_5$ [10,1] 1250
$C_{10}$ [10,2] 18
$C_{11}$ [11,1] 65
$C_3:C_4$ [12,1] 14
$C_{12}$ [12,2] 26
$A_4$ [12,3] 72
$D_6$ [12,4] 174
$C_2\times C_6$ [12,5] 56
$C_{14}$ [14,2] 14
$C_{15}$ [15,1] 24
$C_{16}$ [16,1] 8
$D_8$ [16,7] 4
$SD_{16}$ [16,8] 34
$Q_{16}$ [16,9] 4
$D_9$ [18,1] 3240
$C_{18}$ [18,2] 12
$C_3\times S_3$ [18,3] 75
$C_3:S_3$ [18,4] 3184
$C_3\times C_6$ [18,5] 148
$C_5:C_4$ [20,1] 2
$C_{20}$ [20,2] 4
$D_{10}$ [20,4] 102
$C_7:C_3$ [21,1] 28
$C_{21}$ [21,2] 16
$D_{11}$ [22,1] 30
$C_{22}$ [22,2] 55
$C_{24}$ [24,2] 20
$\SL(2,3)$ [24,3] 10
$D_{12}$ [24,6] 68
$C_3:D_4$ [24,8] 36
$C_3\times D_4$ [24,10] 10
$C_3\times Q_8$ [24,11] 2
$S_4$ [24,12] 16
$C_{25}$ [25,1] 40
$C_3\times C_9$ [27,2] 18
$He_3$ [27,3] 106
$C_9:C_3$ [27,4] 2
$C_3^3$ [27,5] 468
$C_{28}$ [28,2] 12
$C_3\times D_5$ [30,2] 8
$D_{15}$ [30,3] 8
$C_{30}$ [30,4] 12
$C_{33}$ [33,1] 20
$D_{18}$ [36,4] 72
$C_3\times C_3:C_4$ [36,6] 8
$C_3\times C_{12}$ [36,8] 48
$C_3:S_3.C_2$ [36,9] 20
$S_3^2$ [36,10] 22
$C_3\times A_4$ [36,11] 14
$C_6\times S_3$ [36,12] 16
$C_2\times C_3:S_3$ [36,13] 72
$C_6^2$ [36,14] 48
$C_{40}$ [40,2] 8
$C_5:Q_8$ [40,4] 4
$D_{20}$ [40,6] 4
$C_2\times C_7:C_3$ [42,2] 4
$C_{42}$ [42,6] 12
$C_{11}:C_4$ [44,1] 5
$D_{22}$ [44,3] 5
$C_2\times C_{22}$ [44,4] 30
$C_3\times SD_{16}$ [48,26] 4
$\GL(2,3)$ [48,29] 32
$C_9\times S_3$ [54,4] 6
$He_3:C_2$ [54,5] 15
$C_3^2:S_3$ [54,8] 60
$C_2\times He_3$ [54,10] 24
$C_3^2\times S_3$ [54,12] 24
$C_3\times C_3:S_3$ [54,13] 24
$A_5$ [60,5] 20
$C_6\times D_5$ [60,10] 8
$C_3\times C_7:C_3$ [63,3] 12
$C_2^2:D_9$ [72,15] 36
$C_3^2:D_4$ [72,23] 4
$C_3\times \SL(2,3)$ [72,25] 6
$C_3\times D_{12}$ [72,28] 8
$C_3\times C_3:D_4$ [72,30] 4
$F_9$ [72,39] 2
$S_3\wr C_2$ [72,40] 4
$PSU(3,2)$ [72,41] 4
$C_3\times S_4$ [72,42] 2
$C_3:S_4$ [72,43] 24
$C_8:D_5$ [80,6] 8
$C_3\wr C_3$ [81,7] 12
$He_3:C_3$ [81,9] 18
$D_{22}:C_2$ [88,7] 10
$C_3^2:S_3.C_2$ [108,15] 6
$C_3.S_3^2$ [108,17] 4
$C_6^2:C_3$ [108,22] 18
$C_2\times He_3:C_2$ [108,25] 4
$C_3^2:(C_3:C_4)$ [108,37] 4
$C_3\times S_3^2$ [108,38] 2
$C_3^3:C_2^2$ [108,40] 2
$C_3\times \GL(2,3)$ [144,122] 4
$PSU(3,2):C_2$ [144,182] 2
$C_3^2:S_3:C_3$ [162,14] 6
$\PSL(2,7)$ [168,42] 2
$C_3\times A_5$ [180,19] 4
$C_3.S_3\wr C_2$ [216,87] 2
$(C_3\times A_4):C_6$ [216,92] 2
$ASL(2,3)$ [216,153] 4
$S_3^2:S_3$ [216,158] 2
$C_3^3:C_2^2:C_3$ [324,160] 4
$A_6$ [360,118] 4
$AGL(2,3)$ [432,734] 2