ATLAS: Symplectic group S6(2)

Order = 1451520 = 29.34.5.7.
Mult = 2.
Out = 1.

Standard generators

Standard generators of S6(2) are a and b where a is in class 2A, b has order 7 and ab has order 9.
Standard generators of the double cover 2.S6(2) are preimages A and B where B has order 7 and AB has order 9.

Presentations

A presentation of S6(2) on its standard generators is given below.

< a, b | a2 = b7 = (ab)9 = (ab2)12 = [a, b]3 = [a, b2]2 = 1 >.

A shorter, and more coset enumeration friendly, presentation may be obtained by replacing (ab2)12 = 1 with [a, babab]2 = 1.


Representations

The representations of S6(2) available are: The representations of 2.S6(2) available are:

Maximal subgroups


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Last updated 31.05.00,
R.A.Wilson, R.A.Parker and J.N.Bray