Distribution of groups in curves of genus 9

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 4
$C_4$ [4,1] 14
$C_2^2$ [4,2] 25
$S_3$ [6,1] 801
$C_6$ [6,2] 21
$C_7$ [7,1] 36
$C_8$ [8,1] 28
$C_2\times C_4$ [8,2] 101
$D_4$ [8,3] 158
$Q_8$ [8,4] 6
$C_2^3$ [8,5] 315
$C_9$ [9,1] 12
$D_5$ [10,1] 150
$C_{10}$ [10,2] 17
$C_3:C_4$ [12,1] 6
$C_{12}$ [12,2] 26
$A_4$ [12,3] 69
$D_6$ [12,4] 59
$C_2\times C_6$ [12,5] 30
$C_{14}$ [14,2] 18
$C_{15}$ [15,1] 8
$C_4^2$ [16,2] 72
$C_2^2:C_4$ [16,3] 122
$C_4:C_4$ [16,4] 26
$C_2\times C_8$ [16,5] 48
$OD_{16}$ [16,6] 14
$D_8$ [16,7] 264
$SD_{16}$ [16,8] 8
$Q_{16}$ [16,9] 8
$C_2^2\times C_4$ [16,10] 248
$C_2\times D_4$ [16,11] 148
$C_2\times Q_8$ [16,12] 6
$D_4:C_2$ [16,13] 38
$C_2^4$ [16,14] 1120
$D_9$ [18,1] 243
$C_{18}$ [18,2] 3
$C_{19}$ [19,1] 60
$C_5:C_4$ [20,1] 4
$C_{20}$ [20,2] 16
$F_5$ [20,3] 10
$D_{10}$ [20,4] 66
$C_2\times C_{10}$ [20,5] 24
$C_{21}$ [21,2] 30
$C_3:C_8$ [24,1] 6
$C_{24}$ [24,2] 16
$\SL(2,3)$ [24,3] 3
$C_4\times S_3$ [24,5] 14
$D_{12}$ [24,6] 44
$C_2\times C_3:C_4$ [24,7] 4
$C_3:D_4$ [24,8] 10
$C_2\times C_{12}$ [24,9] 8
$C_3\times D_4$ [24,10] 8
$S_4$ [24,12] 39
$C_2\times A_4$ [24,13] 17
$C_2^2\times S_3$ [24,14] 27
$C_2^2\times C_6$ [24,15] 84
$C_{27}$ [27,1] 18
$C_{28}$ [28,2] 12
$C_{30}$ [30,4] 8
$C_4\times C_8$ [32,3] 64
$C_2.OD_{16}$ [32,4] 16
$C_2^2:C_8$ [32,5] 8
$C_2^2.D_4$ [32,6] 22
$OD_{16}.C_2$ [32,8] 4
$D_4:C_4$ [32,9] 32
$C_4\wr C_2$ [32,11] 8
$C_4:C_8$ [32,12] 16
$D_{16}$ [32,18] 32
$SD_{32}$ [32,19] 32
$C_2\times C_2^2:C_4$ [32,22] 96
$C_4\times D_4$ [32,25] 32
$C_2^2\wr C_2$ [32,27] 56
$C_2^2:D_4$ [32,28] 24
$(C_2^2\times C_4):C_2$ [32,30] 16
$C_4.D_4$ [32,31] 16
$C_4:D_4$ [32,34] 72
$C_2\times D_8$ [32,39] 72
$C_2\times SD_{16}$ [32,40] 8
$D_8:C_2$ [32,42] 8
$C_8:C_2^2$ [32,43] 8
$C_2^2\times D_4$ [32,46] 96
$Q_8:C_2^2$ [32,49] 9
$C_4.C_2^3$ [32,50] 1
$C_9:C_4$ [36,1] 6
$C_{36}$ [36,2] 6
$D_{18}$ [36,4] 6
$C_{38}$ [38,2] 18
$C_2\times C_5:C_4$ [40,7] 8
$C_5:D_4$ [40,8] 8
$C_2\times C_{20}$ [40,9] 16
$C_2\times F_5$ [40,12] 2
$C_2^2\times D_5$ [40,13] 24
$C_7\times S_3$ [42,3] 6
$C_8\times S_3$ [48,4] 8
$C_{24}:C_2$ [48,5] 4
$C_3:D_8$ [48,15] 16
$C_6.D_4$ [48,19] 8
$C_3\times C_2^2:C_4$ [48,21] 8
$\GL(2,3)$ [48,29] 12
$A_4:C_4$ [48,30] 4
$C_4\times A_4$ [48,31] 8
$C_2\times \SL(2,3)$ [48,32] 2
$\SL(2,3):C_2$ [48,33] 6
$S_3\times D_4$ [48,38] 4
$C_2\times C_3:D_4$ [48,43] 8
$C_2\times S_4$ [48,48] 10
$C_2^4:C_3$ [48,50] 30
$C_{19}:C_3$ [57,1] 6
$A_5$ [60,5] 3
$C_2^3:C_8$ [64,4] 8
$D_4:C_8$ [64,6] 16
$C_2.(C_2^3.C_4)$ [64,10] 8
$C_4.D_8$ [64,12] 16
$C_2^2:C_4:C_4$ [64,23] 16
$C_4^2:C_4$ [64,34] 4
$C_2^2.D_4.C_2$ [64,35] 8
$(OD_{16}.C_2):C_2$ [64,36] 4
$C_2.C_4:D_4$ [64,73] 64
$(C_2\times D_8):C_2$ [64,128] 32
$D_4:D_4$ [64,134] 4
$C_4\wr C_2:C_2$ [64,135] 4
$C_2\wr C_2^2$ [64,138] 12
$C_4:D_8$ [64,140] 32
$C_8:D_4$ [64,177] 32
$C_{16}:C_2^2$ [64,190] 16
$C_4\times D_9$ [72,5] 12
$D_{10}:C_4$ [80,14] 16
$C_2^2.\SL(2,3)$ [96,3] 8
$(C_2^2\times S_3):C_4$ [96,13] 4
$C_4.S_4$ [96,67] 2
$C_2^2\wr C_2:C_3$ [96,70] 2
$C_4\times S_4$ [96,186] 4
$C_4:S_4$ [96,187] 4
$\SL(2,3):C_2:C_2$ [96,193] 6
$D_4.A_4$ [96,202] 2
$C_2^2:S_4$ [96,227] 9
$S_5$ [120,34] 1
$C_2\times A_5$ [120,35] 2
$C_2^4.D_4$ [128,75] 16
$D_4:D_4.C_2$ [128,134] 4
$C_2.C_2\wr C_4$ [128,136] 4
$C_8:D_4.C_2$ [128,138] 8
$(C_4.C_2^3):C_5$ [160,199] 2
$(C_2^2.\SL(2,3)):C_2$ [192,194] 8
$C_2^2:S_4:C_2$ [192,955] 2
$D_4.S_4$ [192,990] 4
$C_2.C_2^4:D_5$ [320,1582] 4