ChevalleyG2( q )
: algebraic : an algebraic expression, taken to be a prime power
The Chevalley group G2⁡q , for a prime power q, is a generically simple group of Lie type. The groups G2⁡q were studied by Dickson in 1905.
The ChevalleyG2( q ) command returns a permutation group isomorphic to the Chevalley group G2⁡q , for prime powers q≤13. For non-numeric values of the argument q, or for prime powers q larger than 13, a symbolic group representing the group G2⁡q is returned.
Note that the group G2⁡2 is not simple, but its derived subgroup is simple (isomorphic to the simple unitary group PSU⁡3,3 .
For values of q for which G2⁡q is available as a permutation group, the generating permutations have orders 2 and 3 in each case.
CFSG: Steinberg Group A22⁡3=PSU⁡3,3
If the value of the prime power q is too large, or if q is a non-numeric expression, then a symbolic group representing G2⁡q is returned.
Error, (in GroupTheory:-Generators) cannot compute the generators of a symbolic group
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