$\Gamma$

G

$G_v$

$G_e$

s

conditions

$K_{8p}$

$A_{8p}.o$

$A_{8p\text{-1}}.o$

$S_{8p\text{-2}}.o$

2

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

$\mathcal{G}\left(248,5\right)$

$PS{L}_2\left(31\right)$

$A_5$

$S_4$

2

$\mathcal{G}\left(56,10\right)$

$PS{L}_{\text{3}}\left(\text{4}\right)\text{.}o$

$A_6.o$

$3^2:Q_8.o$

2

$1\le o\le {\mathbb{Z}}_4$