ATLAS: Dempwolff group 2^{5}.L_{5}(2)
(nonsplit extension)
Order = 319979520 = 2^{15}.3^{2}.5.7.31.
Mult = 1.
Out = 1.
The page for the image L_{5}(2) is available
here.
The following information is available for 2^{5}.L_{5}(2):
Standard generators of the Dempwolff group 2^{5}.L_{5}(2) are
a and b where a has order 2, b has order 5,
ab has order 21, ababb has order 10, abababbbb has
order 28 and abababbbabb has order 5. These generators map onto
standard generators of L_{5}(2).
NB: There is just one class of involutions of 2^{5}.L_{5}(2)
not in the normal 2^{5} and it maps onto class 2A of L_{5}(2).
A presentation of 2^{5}.L_{5}(2) on its standard generators is given below.
< a, b  a^{2} = b^{5} = (ab)^{21} = [a, b^{2}]^{4} = [a, b^{2}ab^{2}][a, b]^{3} = (ababab^{2})^{2}(abab^{1}ab)^{2}(ab^{1})^{2} = 1 >.
This presentation is available in Magma format as follows:
25L5(2) on a and b.
The representations of 2^{5}.L_{5}(2) available are:

Permutations on 7440 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
 On the cosets of C(a) = 2^{4}.2^{4}.L_{3}(2)  CFs of rep are 1+30+30+124+217+280+868+930+1240+3720.

Permutations on 7440 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 7440 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 69 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 248 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 248 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 248 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 248 over GF(31):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 248 over Z:
a and
b (Meataxe),
a and b (Magma).
Go to main ATLAS (version 2.0) page.
Go to miscellaneous groups page.
Go to old 25L5(2) page (on the L5(2) page)  ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 created on 5th May 1999.
Last updated 27.05.99 by JNB.
Information checked to
Level 1 on 27.05.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.