Embeddings of the groupL(2,13) in groups of lie typeE 6

In this paper we show there is exactly one conjugacy class of subgroups ofE ₆(ℂ) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE ₆. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG ₂. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications to fields of characteristic prime to |L(2, 13)|. Dedicated to John Thompson for his keen interest in broad areas of mathematics and in mathematicians