Distribution of groups in curves of genus 12

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 5
$C_4$ [4,1] 15
$C_2^2$ [4,2] 28
$C_5$ [5,1] 33
$S_3$ [6,1] 7273
$C_6$ [6,2] 40
$C_7$ [7,1] 66
$C_8$ [8,1] 34
$D_4$ [8,3] 365
$Q_8$ [8,4] 13
$C_9$ [9,1] 45
$D_5$ [10,1] 40
$C_{10}$ [10,2] 55
$C_3:C_4$ [12,1] 25
$C_{12}$ [12,2] 47
$A_4$ [12,3] 209
$D_6$ [12,4] 312
$C_2\times C_6$ [12,5] 65
$C_{13}$ [13,1] 105
$D_7$ [14,1] 40
$C_{14}$ [14,2] 71
$C_{15}$ [15,1] 48
$C_{16}$ [16,1] 16
$D_8$ [16,7] 74
$SD_{16}$ [16,8] 4
$Q_{16}$ [16,9] 2
$D_9$ [18,1] 12
$C_{18}$ [18,2] 27
$C_5:C_4$ [20,1] 6
$C_{20}$ [20,2] 10
$F_5$ [20,3] 4
$D_{10}$ [20,4] 6
$C_2\times C_{10}$ [20,5] 38
$C_7:C_3$ [21,1] 9
$C_{21}$ [21,2] 3
$D_{11}$ [22,1] 7320
$C_3:C_8$ [24,1] 2
$C_{24}$ [24,2] 4
$\SL(2,3)$ [24,3] 9
$C_3:Q_8$ [24,4] 4
$D_{12}$ [24,6] 148
$C_3:D_4$ [24,8] 6
$C_3\times D_4$ [24,10] 10
$S_4$ [24,12] 45
$C_{25}$ [25,1] 60
$D_{13}$ [26,1] 42
$C_{26}$ [26,2] 78
$C_{27}$ [27,1] 54
$C_{28}$ [28,2] 30
$D_{14}$ [28,3] 18
$C_2\times C_{14}$ [28,4] 48
$C_5\times S_3$ [30,1] 12
$D_{15}$ [30,3] 16
$C_{30}$ [30,4] 20
$C_{32}$ [32,1] 16
$D_{16}$ [32,18] 8
$SD_{32}$ [32,19] 4
$C_{35}$ [35,1] 24
$C_{36}$ [36,2] 24
$C_2^2:C_9$ [36,3] 6
$D_{18}$ [36,4] 6
$C_{39}$ [39,2] 24
$C_5:C_8$ [40,1] 4
$C_{10}.C_4$ [40,3] 2
$D_{20}$ [40,6] 4
$C_5:D_4$ [40,8] 4
$C_5\times D_4$ [40,10] 4
$F_7$ [42,1] 1
$C_2\times C_7:C_3$ [42,2] 2
$C_7\times S_3$ [42,3] 3
$C_3\times D_7$ [42,4] 3
$D_{21}$ [42,5] 6
$D_{22}$ [44,3] 120
$C_{48}$ [48,2] 8
$D_{24}$ [48,7] 4
$C_{24}.C_2$ [48,8] 4
$C_3:SD_{16}$ [48,16] 4
$C_2.S_4$ [48,28] 2
$C_{50}$ [50,2] 20
$C_{13}:C_4$ [52,1] 6
$D_{13}.C_2$ [52,3] 3
$D_{26}$ [52,4] 6
$C_2\times C_{26}$ [52,5] 36
$C_{11}:C_5$ [55,1] 8
$C_7\times D_4$ [56,9] 12
$C_5\times A_4$ [60,9] 4
$C_{10}\times S_3$ [60,11] 8
$C_5:D_8$ [80,15] 8
$S_3\times D_7$ [84,8] 3
$C_7:A_4$ [84,11] 6
$C_{16}:S_3$ [96,7] 8
$C_{13}:D_4$ [104,8] 12
$F_{11}$ [110,1] 4
$C_5:S_4$ [120,38] 4