ATLAS: Unitary group U_{5}(3)
Order = 258190571520 = 2^{11}.3^{10}.5.7.61.
Mult = 1.
Out = 2.
The page for the group 3^{10}.U_{5}(3) (nonsplit extension)
is available here.
The following information is available for U_{5}(3):
Standard generators for U_{5}(3) are a and b where
a is in class 3A, b has order 5 and ab has order 16.
Standard generators for U_{5}(3):2 are c and d where
c is in class ??, d has order ? and cd has order ??.
NB: Class 3A is the class of transvections in U_{5}(3).
An [outer] automorphism of U_{5}(3) of order 2 can be obtained by
mapping (a, b) to
(a^{1}, b).
< a, b  a^{3} = b^{5} =
[a, bab^{1}ab] =
[a, b^{2}ab^{2}] =
(babababa^{1})^{4} =
(ababa^{1}bab^{2})^{5} = 1 >.
The representations of U_{5}(3) available are:

Dimension 5[a] over GF(9)  the natural representation:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 5[b] over GF(9)  dual of the above:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 10[a] over GF(9)  skew square of 5a:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 10[b] over GF(9)  skew square of 5b:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 10 over GF(3)  reducible over GF(9):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15[a] over GF(9)  symmetric square of 5a:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15[b] over GF(9)  symmetric square of 5b:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 20 over GF(3)  reducible over GF(9):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 24 over GF(3)  adjoint representation:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 30[a] over GF(9)  in 5a × 10a:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 30[b] over GF(9)  in 5b × 10b:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 30 over GF(3)  reducible over GF(9):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 51 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The maximal subgroups of U_{5}(3) are (I reckon) as follows [implementation of word programs not checked]:
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
There is no old U5(3) page in the ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 24th September 2001.
Last updated 24.09.01 by JNB.
Information checked to
Level 0 on 24.09.01 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.