## Distribution of groups in curves of genus 15

Isomorphism class GAP/Magma Group Distinct generating vectors
$C_2$ [2,1] 1
$C_3$ [3,1] 6
$C_4$ [4,1] 27
$C_2^2$ [4,2] 52
$S_3$ [6,1] 65457
$C_6$ [6,2] 67
$C_7$ [7,1] 114
$C_8$ [8,1] 73
$C_2\times C_4$ [8,2] 399
$D_4$ [8,3] 1598
$Q_8$ [8,4] 62
$C_2^3$ [8,5] 1393
$C_9$ [9,1] 78
$D_5$ [10,1] 31250
$C_{10}$ [10,2] 58
$C_{11}$ [11,1] 182
$C_3:C_4$ [12,1] 111
$C_{12}$ [12,2] 103
$A_4$ [12,3] 627
$D_6$ [12,4] 883
$C_2\times C_6$ [12,5] 160
$D_7$ [14,1] 58824
$C_{14}$ [14,2] 48
$C_{15}$ [15,1] 28
$C_{16}$ [16,1] 64
$C_4^2$ [16,2] 400
$C_4:C_4$ [16,4] 136
$C_2\times C_8$ [16,5] 164
$OD_{16}$ [16,6] 60
$D_8$ [16,7] 828
$SD_{16}$ [16,8] 124
$Q_{16}$ [16,9] 28
$C_2\times D_4$ [16,11] 936
$C_2\times Q_8$ [16,12] 84
$D_4:C_2$ [16,13] 336
$D_9$ [18,1] 486
$C_{18}$ [18,2] 39
$C_5:C_4$ [20,1] 4
$C_{20}$ [20,2] 40
$D_{10}$ [20,4] 154
$C_7:C_3$ [21,1] 228
$C_{21}$ [21,2] 36
$C_{22}$ [22,2] 50
$C_3:C_8$ [24,1] 12
$C_{24}$ [24,2] 24
$\SL(2,3)$ [24,3] 14
$C_3:Q_8$ [24,4] 8
$C_4\times S_3$ [24,5] 132
$D_{12}$ [24,6] 52
$C_2\times C_3:C_4$ [24,7] 36
$C_3:D_4$ [24,8] 64
$C_2\times C_{12}$ [24,9] 76
$C_3\times D_4$ [24,10] 28
$S_4$ [24,12] 180
$C_2\times A_4$ [24,13] 54
$C_2^2\times S_3$ [24,14] 196
$C_2^2\times C_6$ [24,15] 364
$C_7:C_4$ [28,1] 78
$D_{14}$ [28,3] 2472
$C_3\times D_5$ [30,2] 4
$D_{15}$ [30,3] 900
$C_{30}$ [30,4] 12
$C_{31}$ [31,1] 160
$C_{32}$ [32,1] 72
$D_4:C_4$ [32,9] 32
$Q_8:C_4$ [32,10] 24
$C_4\wr C_2$ [32,11] 28
$C_8:C_4$ [32,13] 24
$C_2.D_8$ [32,14] 24
$C_2\times C_{16}$ [32,16] 40
$OD_{32}$ [32,17] 12
$D_{16}$ [32,18] 168
$SD_{32}$ [32,19] 20
$C_2\times D_8$ [32,39] 296
$C_2\times SD_{16}$ [32,40] 16
$C_2\times Q_{16}$ [32,41] 16
$D_8:C_2$ [32,42] 24
$C_8:C_2^2$ [32,43] 48
$SD_{16}:C_2$ [32,44] 8
$C_{33}$ [33,1] 90
$C_{35}$ [35,1] 60
$C_{36}$ [36,2] 36
$C_2^2:C_9$ [36,3] 9
$D_{18}$ [36,4] 12
$C_5:C_8$ [40,1] 12
$C_{40}$ [40,2] 16
$C_4\times D_5$ [40,5] 20
$D_{20}$ [40,6] 16
$F_7$ [42,1] 24
$C_2\times C_7:C_3$ [42,2] 4
$C_3\times D_7$ [42,4] 24
$D_{21}$ [42,5] 432
$C_{42}$ [42,6] 12
$C_{44}$ [44,2] 20
$C_{45}$ [45,1] 24
$C_{48}$ [48,2] 16
$C_4^2:C_3$ [48,3] 12
$C_8\times S_3$ [48,4] 8
$C_{24}:C_2$ [48,5] 4
$C_2\times C_3:C_8$ [48,9] 8
$C_3:OD_{16}$ [48,10] 4
$C_4\times C_{12}$ [48,20] 96
$C_3\times C_4:C_4$ [48,22] 24
$C_2.S_4$ [48,28] 2
$\GL(2,3)$ [48,29] 13
$C_2\times \SL(2,3)$ [48,32] 2
$\SL(2,3):C_2$ [48,33] 10
$C_2\times D_{12}$ [48,36] 16
$D_{12}:C_2$ [48,37] 4
$S_3\times D_4$ [48,38] 8
$D_4:S_3$ [48,39] 4
$C_2\times C_3:D_4$ [48,43] 32
$C_2\times S_4$ [48,48] 14
$C_7^2$ [49,2] 336
$C_{11}:C_5$ [55,1] 4
$C_4\times D_7$ [56,4] 96
$D_{28}$ [56,5] 96
$D_{14}:C_2$ [56,7] 96
$C_2^2\times D_7$ [56,12] 288
$C_{15}:C_4$ [60,3] 8
$C_{60}$ [60,4] 8
$A_5$ [60,5] 30
$D_{30}$ [60,12] 8
$C_{62}$ [62,2] 30
$C_2.Q_{32}$ [64,39] 16
$OD_{32}:C_2$ [64,41] 4
$C_2.D_{16}$ [64,47] 16
$C_2.SD_{32}$ [64,48] 16
$C_2\times C_{32}$ [64,50] 32
$OD_{64}$ [64,51] 8
$C_2\times D_{16}$ [64,186] 32
$D_{16}:C_2$ [64,189] 8
$C_{16}:C_2^2$ [64,190] 8
$C_{11}\times S_3$ [66,1] 10
$C_7\times D_5$ [70,1] 12
$C_2^2:D_9$ [72,15] 12
$C_2\times C_2^2:C_9$ [72,16] 3
$C_8\times D_5$ [80,4] 16
$C_{40}:C_2$ [80,5] 8
$C_7:C_{12}$ [84,1] 4
$S_3\times D_7$ [84,8] 24
$C_{31}:C_3$ [93,1] 10
$D_{12}:C_4$ [96,12] 8
$C_3:(D_4:C_4)$ [96,16] 16
$C_4^2:C_3:C_2$ [96,64] 2
$\SL(2,3):C_4$ [96,66] 4
$C_4.S_4$ [96,67] 4
$(C_2.S_4):C_2$ [96,192] 4
$\SL(2,3):C_2:C_2$ [96,193] 4
$C_7\times D_7$ [98,3] 18
$D_4\times D_7$ [112,31] 48
$D_{28}:C_2$ [112,34] 48
$\SL(2,5)$ [120,5] 2
$C_4\times D_{15}$ [120,27] 16
$C_2\times A_5$ [120,35] 2
$C_4.D_4:C_4$ [128,147] 32
$C_4.D_4:C_4$ [128,150] 8
$C_2\times C_2^2:D_9$ [144,109] 6
$C_7:(C_7:C_3)$ [147,5] 12
$C_7:\SL(2,3)$ [168,23] 12
$\PSL(2,7)$ [168,42] 2
$F_8:C_3$ [168,43] 4
$C_4.A_5$ [240,93] 4
$C_7^2:S_3$ [294,7] 6
$Q_8.F_7$ [336,134] 12
$SO(3,7)$ [336,208] 1
$\PSL(2,8)$ [504,156] 3