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Twisted Chevalley Groups

Twisted Chevalley groups are finite groups of Lie-type. Small members of these families need not be simple. The following table summarizes some of these groups and their group orders. In the table, q denotes a prime power and the superscript denotes the order of the twisting automorphism. A prime denotes the commutator subgroup.

grouporder
^3D_4(q)q^(12)(q^2-1)(q^8+q^4+1)(q^6-1)
^2F_4(2^(2n+1)) (n>0)(2^(2n+1))^(12)(2^(2n+1)-1)((2^(2n+1))^3+1)((2^(2n+1))^4-1)((2^(2n+1))^6+1)
^2F_4(2)^'2^(11)·3^3·5^2·13
^2G_2(3^(2n+1)) (n>0)(3^(2n+1))^3(3^(2n+1)-1)((3^(2n+1))^3+1)
^2G_2(3)^'2^3·3^2·7
^2B_2(2^(2n+1)) (n>0)(2^(2n+1))^2(2^(2n+1)-1)((2^(2n+1))^2+1)

See also

Chevalley Groups, Finite Group, Ree Group, Simple Group, Tits Group

This entry contributed by Margherita Barile

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References

Gorenstein, D. "Known Simple Groups." Ch. 17 in Finite Groups, 2nd ed. New York: Chelsea, pp. 490-494, 1980.Gorenstein, D.; Lyons, R.; and Solomon, R. The Classification of the Finite Simple Groups. Providence, RI: American Mathematical Society, 1994. https://bookstore.ams.org/surv-40-1.Wilson, R. A.; Parker, R. A.; and Bray, J. N. "ATLAS: Exceptional Groups of Lie Type." https://brauer.maths.qmul.ac.uk/Atlas/exc/.

Referenced on Wolfram|Alpha

Twisted Chevalley Groups

Cite this as:

Weisstein, Eric W., with contributions by Margherita Barile. "Twisted Chevalley Groups." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TwistedChevalleyGroups.html

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