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.
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Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 8th December 1999.
Last updated 15.04.05 by RAW.
R.A.Wilson, S.J.Nickerson and J.N.Bray.