2E6 (mathematics)
In mathematics, 2E6 is a family of Steinberg or twisted Chevalley groups. It is a quasi-split form of E6, depending on a quadratic extension of fields K⊂L. Unfortunately the notation for the group is not standardized, as some authors write it as 2E6 and some as 2E6.
Over finite fields these groups form one of the 18 infinite families of finite simple groups, and were introduced independently by and.
Over finite fields
The group 2E6 has orderq36
/.
This is similar to the order q36
/
of E6.
Its Schur multiplier has order except for q=2, i. e. 2E6, when it has order 12 and is a product of cyclic groups of orders 2,2,3. One of the exceptional double covers of 2E6 is a subgroup of the baby monster group,
and the exceptional central extension by the elementary abelian group of order 4 is a subgroup of the monster group.
The outer automorphism group has order · f where q2 = pf.