Distribution of groups in curves of genus 11

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] 33
$S_3$ [6,1] 1602
$C_6$ [6,2] 31
$C_8$ [8,1] 27
$C_2\times C_4$ [8,2] 159
$D_4$ [8,3] 286
$Q_8$ [8,4] 62
$C_2^3$ [8,5] 525
$C_9$ [9,1] 24
$D_5$ [10,1] 7812
$C_{10}$ [10,2] 24
$C_3:C_4$ [12,1] 41
$C_{12}$ [12,2] 29
$A_4$ [12,3] 48
$D_6$ [12,4] 257
$C_2\times C_6$ [12,5] 69
$C_{15}$ [15,1] 16
$C_{16}$ [16,1] 20
$C_4^2$ [16,2] 96
$C_4:C_4$ [16,4] 24
$C_2\times C_8$ [16,5] 64
$OD_{16}$ [16,6] 22
$D_8$ [16,7] 28
$SD_{16}$ [16,8] 28
$Q_{16}$ [16,9] 12
$C_2\times D_4$ [16,11] 212
$C_2\times Q_8$ [16,12] 20
$D_4:C_2$ [16,13] 89
$C_{18}$ [18,2] 6
$C_5:C_4$ [20,1] 40
$C_{20}$ [20,2] 8
$F_5$ [20,3] 82
$D_{10}$ [20,4] 660
$D_{11}$ [22,1] 605
$C_{22}$ [22,2] 5
$C_{23}$ [23,1] 88
$C_{24}$ [24,2] 12
$\SL(2,3)$ [24,3] 12
$C_4\times S_3$ [24,5] 20
$D_{12}$ [24,6] 48
$C_2\times C_3:C_4$ [24,7] 20
$C_3:D_4$ [24,8] 12
$C_2\times C_{12}$ [24,9] 36
$C_3\times D_4$ [24,10] 4
$S_4$ [24,12] 32
$C_2\times A_4$ [24,13] 21
$C_2^2\times S_3$ [24,14] 144
$C_3\times D_5$ [30,2] 12
$D_{15}$ [30,3] 216
$C_{30}$ [30,4] 8
$D_4:C_4$ [32,9] 24
$C_4\wr C_2$ [32,11] 12
$C_8.C_4$ [32,15] 8
$C_2\times C_{16}$ [32,16] 16
$OD_{32}$ [32,17] 4
$C_2\times D_8$ [32,39] 16
$C_2\times SD_{16}$ [32,40] 16
$D_8:C_2$ [32,42] 12
$C_8:C_2^2$ [32,43] 8
$SD_{16}:C_2$ [32,44] 4
$C_{33}$ [33,1] 10
$C_{10}.C_4$ [40,3] 6
$C_4\times D_5$ [40,5] 48
$D_{20}$ [40,6] 48
$C_5:D_4$ [40,8] 48
$C_2\times F_5$ [40,12] 30
$C_2^2\times D_5$ [40,13] 144
$C_{11}:C_4$ [44,1] 10
$C_{44}$ [44,2] 10
$D_{22}$ [44,3] 10
$C_{46}$ [46,2] 22
$C_4\times C_3:C_4$ [48,11] 16
$C_6.Q_8$ [48,12] 8
$C_{12}:C_4$ [48,13] 8
$C_2\times C_{24}$ [48,23] 16
$C_3\times OD_{16}$ [48,24] 4
$C_2.S_4$ [48,28] 1
$\GL(2,3)$ [48,29] 14
$C_2\times \SL(2,3)$ [48,32] 8
$C_2\times D_{12}$ [48,36] 16
$D_{12}:C_2$ [48,37] 4
$S_3\times D_4$ [48,38] 4
$C_2\times S_4$ [48,48] 8
$A_5$ [60,5] 18
$C_3\times F_5$ [60,6] 2
$C_3:F_5$ [60,7] 4
$S_3\times D_5$ [60,8] 12
$D_8.C_4$ [64,40] 8
$(C_2\times D_8).C_2$ [64,42] 8
$C_3\times D_{11}$ [66,2] 10
$D_5:C_8$ [80,28] 8
$D_{10}.C_4$ [80,29] 4
$C_4\times F_5$ [80,30] 8
$C_4:F_5$ [80,31] 4
$D_4\times D_5$ [80,39] 24
$D_{10}.C_2^2$ [80,42] 24
$C_4\times D_{11}$ [88,4] 20
$(C_2\times C_{24}):C_2$ [96,28] 16
$(C_3\times OD_{16}):C_2$ [96,32] 8
$C_2\times \GL(2,3)$ [96,189] 8
$\GL(2,3):C_2$ [96,190] 2
$S_5$ [120,34] 2
$C_2\times A_5$ [120,35] 18
$S_3\times F_5$ [120,36] 2
$D_4:F_5$ [160,82] 8
$(C_5\times Q_8):C_4$ [160,85] 8
$C_2\times S_5$ [240,189] 2