ATLAS: Unitary group U7(2)
Order = 227787103272960 = 221.38.5.7.11.43.
Mult = 1.
Out = 2.
The page for the group 214.U7(2) (nonsplit extension)
is available here.
The following information is available for U7(2):
Standard generators of U7(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 U7(2).
An outer automorphism of U7(2) may be obtained by mapping
(a, b) to (a, b-1).
A presentation of U7(2) on its standard generators is given below.
< a, b | a2 = b7 = (ab)33 = [a, b]3 = [a, b2]3 = [a, b3]3 = [a, bab]2 = [a, b2ab2]2 = [a, bab2]3 = (abab-3ab-3)8 = 1 >.
This presentation is available in Magma format as follows:
U7(2) on a and b.
The representations of U7(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 U7(2) are as follows [from Kleidman's list]:
-
21+10:(3 × U5(2)), with generators
a, bab^3ab.
Order: 84085309440.
Index: 2709.
-
3.U6(2).3, with generators
a, bab^5.
Order: 82771476480.
Index: 2752.
-
29+6:3.L3(4).3.
Order: 5945425920.
Index: 38313.
-
24+12.(A5 × 31+2:2A4).
Order: 2548039680.
Index: 89397.
-
3 × S3 × U5(2).
Order: 246343680.
Index: 924672.
-
31+2:2A4 × U4(2).
Order: 16796160.
Index: 13561856.
-
36:S7, with generators
a, babab^3abab^4.
Order: 3674160.
Index: 61997056.
-
43:7 = F301.
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.