Conjugacy of Alt_5 and SL(2, 5) Subgroups of E_6(C), F_4(C) and a Subgroup of E_8(C) of Type A_2E_6
Journal of Algebra
We classify Alt5 and SL2; 5 subgroups of E6 and F4 up to conjugacy. We then use our results to answer conjugacy questions about ALT5 and SL2; 5 subgroups of E8 which were not resolved in earlier work.
Frey, D. D. (1998). Conjugacy of Alt_5 and SL(2, 5) subgroups of E_6(C), F_4(C) and a subgroup of E_8(C) of type A_2E_6. Journal of Algebra, 202, 414-454.