Distribution of groups in curves of genus 2

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 1
$C_4$ [4,1] 1
$C_2^2$ [4,2] 3
$C_5$ [5,1] 4
$S_3$ [6,1] 2
$C_6$ [6,2] 3
$C_8$ [8,1] 2
$D_4$ [8,3] 1
$Q_8$ [8,4] 1
$C_{10}$ [10,2] 4
$C_3:C_4$ [12,1] 1
$D_6$ [12,4] 1
$C_2\times C_6$ [12,5] 6
$SD_{16}$ [16,8] 2
$\SL(2,3)$ [24,3] 1
$C_3:D_4$ [24,8] 2
$\GL(2,3)$ [48,29] 2