Distribution of groups in curves of genus 13

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 6
$C_4$ [4,1] 20
$C_2^2$ [4,2] 42
$S_3$ [6,1] 32728
$C_6$ [6,2] 56
$C_8$ [8,1] 57
$C_2\times C_4$ [8,2] 276
$D_4$ [8,3] 894
$Q_8$ [8,4] 62
$C_2^3$ [8,5] 917
$C_9$ [9,1] 26
$C_3^2$ [9,2] 368
$D_5$ [10,1] 400
$C_{10}$ [10,2] 52
$C_3:C_4$ [12,1] 32
$C_{12}$ [12,2] 76
$A_4$ [12,3] 471
$D_6$ [12,4] 1390
$C_2\times C_6$ [12,5] 134
$D_7$ [14,1] 588
$C_{14}$ [14,2] 39
$C_{15}$ [15,1] 36
$C_{16}$ [16,1] 40
$C_4^2$ [16,2] 228
$C_2^2:C_4$ [16,3] 442
$C_4:C_4$ [16,4] 82
$C_2\times C_8$ [16,5] 134
$OD_{16}$ [16,6] 48
$D_8$ [16,7] 320
$SD_{16}$ [16,8] 148
$Q_{16}$ [16,9] 8
$C_2^2\times C_4$ [16,10] 884
$C_2\times D_4$ [16,11] 608
$C_2\times Q_8$ [16,12] 54
$D_4:C_2$ [16,13] 200
$C_2^4$ [16,14] 4620
$D_9$ [18,1] 144
$C_{18}$ [18,2] 36
$C_3\times S_3$ [18,3] 125
$C_3:S_3$ [18,4] 1548
$C_3\times C_6$ [18,5] 150
$C_5:C_4$ [20,1] 16
$C_{20}$ [20,2] 24
$D_{10}$ [20,4] 16
$C_2\times C_{10}$ [20,5] 72
$C_{21}$ [21,2] 12
$C_{24}$ [24,2] 8
$\SL(2,3)$ [24,3] 21
$C_3:Q_8$ [24,4] 16
$C_4\times S_3$ [24,5] 60
$D_{12}$ [24,6] 1296
$C_2\times C_3:C_4$ [24,7] 28
$C_3:D_4$ [24,8] 88
$C_2\times C_{12}$ [24,9] 80
$C_3\times D_4$ [24,10] 24
$S_4$ [24,12] 233
$C_2\times A_4$ [24,13] 109
$C_2^2\times S_3$ [24,14] 500
$C_2^2\times C_6$ [24,15] 112
$D_{13}$ [26,1] 1014
$C_{26}$ [26,2] 6
$C_{27}$ [27,1] 36
$C_7:C_4$ [28,1] 6
$C_{28}$ [28,2] 36
$D_{14}$ [28,3] 177
$C_2\times C_{14}$ [28,4] 36
$C_5\times S_3$ [30,1] 8
$C_3\times D_5$ [30,2] 4
$D_{15}$ [30,3] 400
$C_{30}$ [30,4] 24
$C_2.C_4^2$ [32,2] 112
$C_2^2:C_8$ [32,5] 48
$C_2^2.D_4$ [32,6] 30
$C_2^3.C_4$ [32,7] 44
$D_4:C_4$ [32,9] 28
$C_4\wr C_2$ [32,11] 20
$C_2\times C_{16}$ [32,16] 32
$OD_{32}$ [32,17] 8
$D_{16}$ [32,18] 64
$C_2\times C_4^2$ [32,21] 256
$C_2\times C_4:C_4$ [32,23] 64
$(C_2\times C_4):C_4$ [32,24] 64
$C_4\times D_4$ [32,25] 64
$C_2^2\wr C_2$ [32,27] 224
$C_2^2:D_4$ [32,28] 136
$C_2^2:Q_8$ [32,29] 32
$(C_2^2\times C_4):C_2$ [32,30] 32
$C_4.D_4$ [32,31] 32
$C_4^2:C_2$ [32,33] 32
$C_4:D_4$ [32,34] 384
$C_2^2\times C_8$ [32,36] 96
$C_2\times OD_{16}$ [32,37] 24
$OD_{16}:C_2$ [32,38] 24
$C_2\times D_8$ [32,39] 96
$C_2\times SD_{16}$ [32,40] 8
$D_8:C_2$ [32,42] 32
$C_8:C_2^2$ [32,43] 32
$SD_{16}:C_2$ [32,44] 4
$C_2^2\times D_4$ [32,46] 320
$C_2\times D_4:C_2$ [32,48] 80
$Q_8:C_2^2$ [32,49] 36
$C_{36}$ [36,2] 12
$C_2^2:C_9$ [36,3] 6
$D_{18}$ [36,4] 72
$C_3\times C_3:C_4$ [36,6] 6
$C_3\times C_{12}$ [36,8] 48
$C_3:S_3.C_2$ [36,9] 36
$S_3^2$ [36,10] 44
$C_3\times A_4$ [36,11] 78
$C_6\times S_3$ [36,12] 28
$C_2\times C_3:S_3$ [36,13] 312
$C_{39}$ [39,2] 12
$C_2\times C_{20}$ [40,9] 32
$C_{42}$ [42,6] 12
$C_3\times C_{15}$ [45,2] 96
$C_4^2:C_3$ [48,3] 24
$C_8:S_3$ [48,6] 64
$D_{24}$ [48,7] 64
$D_6:C_4$ [48,14] 64
$C_3\times C_2^2:C_4$ [48,21] 16
$\GL(2,3)$ [48,29] 12
$C_4\times A_4$ [48,31] 6
$C_2\times \SL(2,3)$ [48,32] 4
$\SL(2,3):C_2$ [48,33] 16
$C_2\times C_4\times S_3$ [48,35] 32
$C_2\times D_{12}$ [48,36] 144
$D_{12}:C_2$ [48,37] 16
$S_3\times D_4$ [48,38] 32
$C_2\times C_3:D_4$ [48,43] 16
$C_2\times S_4$ [48,48] 54
$C_2^2\times A_4$ [48,49] 32
$C_2^4:C_3$ [48,50] 120
$C_2^3\times S_3$ [48,51] 224
$C_{13}:C_4$ [52,1] 12
$C_{52}$ [52,2] 12
$D_{26}$ [52,4] 12
$C_{54}$ [54,2] 18
$C_2\times C_7:C_4$ [56,6] 12
$D_{14}:C_2$ [56,7] 12
$C_2\times C_{28}$ [56,8] 24
$C_2^2\times D_7$ [56,12] 36
$A_5$ [60,5] 2
$S_3\times D_5$ [60,8] 8
$C_2^2.SD_{16}$ [64,8] 8
$C_2.(C_2^2.D_4)$ [64,9] 16
$(C_2\times OD_{16}).C_2$ [64,18] 16
$(C_2\times C_4).D_4$ [64,20] 32
$C_2.D_4:C_4$ [64,21] 32
$C_2^2:C_{16}$ [64,29] 16
$C_2^3.C_8$ [64,30] 4
$D_4.C_8$ [64,31] 8
$C_2\wr C_4$ [64,32] 4
$(C_2^2\times C_4):C_4$ [64,33] 8
$(C_2\times D_8):C_2$ [64,128] 32
$C_4:C_4.C_2^2$ [64,130] 16
$D_4:D_4$ [64,134] 16
$C_2^2:D_8$ [64,147] 16
$C_2.C_8:C_2^2$ [64,150] 16
$C_8:C_2^2:C_2$ [64,153] 8
$C_2\times C_2^2:C_9$ [72,16] 6
$C_2.S_3^2$ [72,21] 4
$C_3^2:D_4$ [72,23] 32
$C_{12}\times S_3$ [72,27] 8
$S_3\wr C_2$ [72,40] 4
$C_3\times S_4$ [72,42] 8
$C_3:S_4$ [72,43] 18
$S_3\times A_4$ [72,44] 18
$C_2\times C_3:S_3.C_2$ [72,45] 4
$C_2\times S_3^2$ [72,46] 20
$C_6\times A_4$ [72,47] 18
$C_3\times D_{13}$ [78,4] 12
$C_3\times D_{15}$ [90,7] 8
$C_2^2.\SL(2,3)$ [96,3] 8
$C_2\times C_4^2:C_3$ [96,68] 8
$C_2^2\wr C_2:C_3$ [96,70] 4
$C_2^3.A_4$ [96,71] 4
$C_2^2:D_{12}$ [96,89] 64
$C_4:D_{12}$ [96,102] 64
$C_8:D_6$ [96,115] 32
$C_4:S_4$ [96,187] 32
$D_4\times A_4$ [96,197] 4
$C_2\times \SL(2,3):C_2$ [96,200] 16
$C_2^2\times S_4$ [96,226] 16
$C_4\times D_{13}$ [104,5] 24
$D_{14}:C_4$ [112,13] 24
$C_2\times A_5$ [120,35] 2
$(C_2^2\times C_4).D_4$ [128,71] 8
$C_2^2:D_8.C_2$ [128,79] 16
$S_3^2:C_4$ [144,115] 4
$S_3\times S_4$ [144,183] 3
$A_4^2$ [144,184] 4
$C_2\times S_3\times A_4$ [144,190] 4
$C_3\times A_5$ [180,19] 2
$A_4\times S_4$ [288,1024] 2
$S_3\times A_5$ [360,121] 2