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GroupTheory

 Ree2F4

 Calling Sequence Ree2F4( q )

Parameters

 q - : {posint,algebraic} : an odd power of $2$, or an expression

Description

 • The Ree groups ${}^{2}F_{4}\left(q\right)$ , for an odd power $q$ of $2$, are a series of (typically) simple groups of Lie type, first constructed by R. Ree. They are defined only for $q={2}^{2e+1}$ an odd power of $2$ (where, here, $0\le e$).
 • The Ree2F4( q ) command constructs a symbolic group representing the large Ree group ${}^{2}F_{4}\left(q\right)$ .
 • The large Ree groups ${}^{2}F_{4}\left(q\right)$ are simple for all odd powers $q$ of $2$ greater than $2$, but ${}^{2}F_{4}\left(2\right)$ is not simple. Its derived subgroup is the simple Tits group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Ree2F4}\left(2\right)$
 ${G}{≔}{}^{{2}}{\mathbit{F}}_{{4}}{}\left({2}\right)$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${35942400}$ (2)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsSimple}\left(\mathrm{Ree2F4}\left(8\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{MinPermRepDegree}\left(\mathrm{Ree2F4}\left(8\right)\right)$
 ${1210323465}$ (5)
 > $\mathrm{IsSimple}\left(\mathrm{Ree2F4}\left(q\right)\right)$
 $\left\{\begin{array}{cc}{\mathrm{false}}& {q}{=}{2}\\ {\mathrm{true}}& {\mathrm{otherwise}}\end{array}\right\$ (6)
 > $\mathrm{ClassNumber}\left(\mathrm{Ree2F4}\left(q\right)\right)$
 ${{q}}^{{4}}{+}{4}{}{{q}}^{{2}}{+}{17}$ (7)
 Compatibility