Linear group L3(5)


Order = 372 000 = 25.3.53.31.
Mult = 1.
Out = 2.

Robert Wilson's ATLAS page for L3(5) is available here.

L3(5): Length 59, 2-generator, 5-relator.

< x, y | x3 = y5 = xyx-1yxy-2x-1yxyx-1y-2 = [y, [y, yx]] = xyxyxy-1xy2xy2xy-1xyx-1y-2x-1y-1 = 1 >

Remark: x and y are R.A.Wilson's standard generators for L3(5). The presentation is available in MAGMA code here. (This applies to the subgroups below too.) I have included a redundant relation in the presentation to aid coset enumeration.

Some subgroups:

Realisation: As 3 × 3 matrices over GF(5) in MAGMA format.


L3(5):2: Length ??, 2-generator, ?-relator.


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Last updated 26th August, 1997
John N. Bray