to $PGL_2(7)$... –  Anvita Apr 20 '11 at 15:21 feedback 1 Answer active oldest votes up vote 1 down vote A quick look at the ATLAS shows that $A_7$ has two conjugacy classes (of size 15 each) of subgroups isomorphic to $PSL_2(7)$ which fuse into one class in $S_7$. So, there