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Chevalley Groups

The Chevalley groups are the finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special unitary group), PSp(2n,q) (the projective symplectic group), and POmega^epsilon(n,q).

The following table lists exceptional (untwisted) Chevalley groups.

grouporder
E_6(q)(q^(36)(q^2-1)(q^5-1)(q^6-1)(q^8-1)(q^9-1)(q^(12)-1))/(GCD(3,q-1))
E_7(q)(q^(63)(q^2-1)(q^6-1)(q^8-1)(q^(10)-1)(q^(12)-1)(q^(14)-1)(q^(18)-1))/(GCD(2,q-1))
E_8(q)q^(120)(q^2-1)(q^8-1)(q^(12)-1)(q^(14)-1)(q^(18)-1)(q^(20)-1)(q^(24)-1)(q^(30)-1)
F_4(q)q^(24)(q^2-1)(q^6-1)(q^8-1)(q^(12)-1)
G_2(q) (q>2)q^6(q^2-1)(q^6-1)

See also

Projective Special Linear Group, Projective Special Unitary Group, Projective Symplectic Group, Twisted Chevalley Groups

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References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, 1985.Wilson, R. A. "ATLAS of Finite Group Representation." http://brauer.maths.qmul.ac.uk/Atlas/v3/exc/.Wilson, R. A.; Parker, R. A.; and Bray, J. N. "ATLAS: Exceptional Groups of Lie Type." http://web.mat.bham.ac.uk/atlas/v2.0/exc/.

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Chevalley Groups

Cite this as:

Weisstein, Eric W. "Chevalley Groups." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChevalleyGroups.html

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