Chevalley Groups of Type E8
Chevalley (1955) showed that the points of the (split) algebraic group E8 (see above) over a finite field with q elements form a finite Chevalley group, generally written E8(q), which is simple for any q, and constitutes one of the infinite families addressed by the classification of finite simple groups. Its number of elements is given by the formula (sequence A008868 in OEIS):
The first term in this sequence, the order of E8(2), namely 337804753143634806261388190614085595079991692242467651576160 ≈ 3.38×1074, is already larger than the size of the Monster group. This group E8(2) is the last one described (but without its character table) in the ATLAS of Finite Groups.
The Schur multiplier of E8(q) is trivial, and its outer automorphism group is that of field automorphisms (i.e., cyclic of order f if q=pf where p is prime).
Lusztig (1979) described the unipotent representations of finite groups of type E8.
Read more about this topic: E8 (mathematics)
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