ATLAS: Nonsplit extension 2^{14}.U_{7}(2)
Order = 3732063900024176640 = 2^{35}.3^{8}.5.7.11.43.
Mult = 1.
Out = 2.
The page for the image U_{7}(2) is available
here.
The following information is available for 2^{14}.U_{7}(2):
Standard generators of 2^{14}.U_{7}(2) are a and
b where a is in class 2C, b has order 7 and ab has order 33. No extra conditions (such as abb having order 45) are required. These generators map onto standard generators of U_{7}(2).
Standard generators of 2^{14}.U_{7}(2):2 are not defined.
Note that 2^{14}.U_{7}(2) has a unique conjugacy class of subgroups of index 10836, and we may take a to be a central involution in such a subgroup. In fact, this subgroup turns out to be C(a). Also, a happens to be in a class of 3transpositions, and a commutes with 2644 of its conjugates. The orbits of C(a) [acting by conjugation] on the conjugates of a have sizes 1, 3, 2640 and 8192.
Remark: As far as we know, this group was discovered by J.I.Hall. He also discovered its 3transposition property.
An outer automorphism of 2^{14}.U_{7}(2) may be obtained by mapping
(a, b) to (a, b^{1}).
A presentation of 2^{14}.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}abab^{2}ab^{2})^{6} = 1 >.
This presentation is available in Magma format as follows:
2^{14}.U_{7}(2) on a and b.
The representations of 2^{14}.U_{7}(2) available are:

Permutations on 10836 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 the smallest degree of a faithful permutation representation.

Dimension ?? over GF(4)  NOT YET AVAILABLE:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
Go to main ATLAS (version 2.0) page.
Go to miscellaneous groups page.
There is no old 214U7(2) page or U7(2) page in the ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 created on 10th December 1999.
Last updated 02.08.00 by JNB.
Information checked to
Level 0 on 10.12.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.