ATLAS: Symplectic group S10(2)

Order = 24815256521932800 = 225.36.52.7.11.17.31.
Mult = 1.
Out = 1.

The following information is available for S10(2):


Standard generators

Standard generators of S10(2) are a and b where a is in class 2A, b has order 11 and ab has order 15.
NB: Class 2A is the class of transvections in the natural 10-dimensional representation of S10(2)

Presentation

A presentation for S10(2) in terms of its standard generators is given below.

< a, b | a2 = b11 = (ab)15 = (ab5)18 = [a, b]3 = [a, b2]2 = [a, b3]2 = [a, b4]2 = [a, b5]3 = [a, (ab)5]2 = 1 >.


Representations

The representations of S10(2) available are:

Maximal subgroups

The maximal subgroups of S10(2) include the following.

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Last updated 24th March 1998,
R.A.Wilson, R.A.Parker and J.N.Bray