ATLAS: Linear group L6(2)

Order = 20158709760 = 215.34.5.72.31.
Mult = 1.
Out = 2.

Standard generators

Standard generators of L6(2) are a and b where a is in class 2A, b is in class 6F, ab has order 63 and abb has order 6.

Standard generators of L6(2):2 are c and d where c is in class 2D, d is in class 7CD (i.e. the class of 7-elements with fixed points in the natural representation) cd has order 30, and cdd has order 14.

To obtain standard generators for L6(2) from those for L6(2):2 run this program.

The outer automorphism of L6(2) may be realised by running this program.

Black box algorithms

To obtain standard generators of L6(2): To obtain standard generators of L6(2).2:

Representations

The representations of L6(2) available are: The representations of L6(2):2 available are:

Maximal subgroups

The maximal subgroups of L6(2) are:
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Last updated 14th August 1998,
R.A.Wilson, R.A.Parker and J.N.Bray