$\Gamma$

G

$G_v$

$G_e$

s

conditions

$\mathcal{G}\left(57,6\right)$

$PS{L}_2\left(19\right)$

$A_5$

$D_{20}$

2

$\mathcal{G}\left(117,36\right)$

$PS{L}_4\left(3\right)$

$PS{U}_4\left(2\right):2$

$\left(4\times A_6\right):2$

1

$\mathcal{G}\left(891,512\right)$

$PS{U}_6\left(2\right).o$

$2^9:PS{L}_3\left(4\right).o$

$\left(PS{L}_3\left(4\right):2\right).o$

1

$1\le o\le S_3$

$\mathcal{G}\left(351,126\right)$

$P{\Omega }_7\left(3\right).o$

$\left(2PS{U}_4\left(3\right):2\right).o$

$\left(\left(2^2\times PS{U}_4\left(2\right)\right):2\right).o$

1

$1\le o\le {\mathbb{Z}}_2$

$\mathcal{G}\left(1107,378\right)$

$P{\Omega }_8^{-}\left(3\right).o$

$\left({\Omega }_7\left(3\right):2\right).o$

$\left(\left(4\times PS{L}_4\left(3\right)\right):2\right).o$

1

$1\le o\le {\mathbb{Z}}_2^2$