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]:
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Version 2.0 created on 24th September 2001.
Last updated 15.04.05 by RAW.
R.A.Wilson, S.J.Nickerson and J.N.Bray.