ATLAS: Unitary group U_{7}(2)
Order = 227787103272960 = 2^{21}.3^{8}.5.7.11.43.
Mult = 1.
Out = 2.
The page for the group 2^{14}.U_{7}(2) (nonsplit extension)
is available here.
The following information is available for U_{7}(2):
Standard generators of U_{7}(2) are a and
b where a is in class 2A, b has order 7, ab has order 33 and abb has order 45.
NB: Class 2A is the class of transvections of U_{7}(2).
An outer automorphism of U_{7}(2) may be obtained by mapping
(a, b) to (a, b^{1}).
A presentation of U_{7}(2) on its standard generators is given below.
< a, b  a^{2} = b^{7} = (ab)^{33} = [a, b]^{3} = [a, b^{2}]^{3} = [a, b^{3}]^{3} = [a, bab]^{2} = [a, b^{2}ab^{2}]^{2} = [a, bab^{2}]^{3} = (abab^{3}ab^{3})^{8} = 1 >.
This presentation is available in Magma format as follows:
U7(2) on a and b.
The representations of U_{7}(2) available are:

Permutations on 2709 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 2752 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 7 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The maximal subgroups of U_{7}(2) are as follows [from Kleidman's list]:

2^{1+10}:(3 × U_{5}(2)), with generators
a, bab^3ab.
Order: 84085309440.
Index: 2709.

3.U_{6}(2).3, with generators
a, bab^5.
Order: 82771476480.
Index: 2752.

2^{9+6}:3.L_{3}(4).3.
Order: 5945425920.
Index: 38313.

2^{4+12}.(A_{5} × 3^{1+2}:2A_{4}).
Order: 2548039680.
Index: 89397.

3 × S_{3} × U_{5}(2).
Order: 246343680.
Index: 924672.

3^{1+2}:2A_{4} × U_{4}(2).
Order: 16796160.
Index: 13561856.

3^{6}:S_{7}, with generators
a, babab^3abab^4.
Order: 3674160.
Index: 61997056.

43:7 = F_{301}.
Order: 301.
Index: 756767784960.
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 8th December 1999.
Last updated 02.08.00 by JNB.
Information checked to
Level 0 on 09.12.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.