ATLAS: Dempwolff group 25.L5(2)
(nonsplit extension)
Order = 319979520 = 215.32.5.7.31.
Mult = 1.
Out = 1.
The page for the image L5(2) is available
here.
The following information is available for 25.L5(2):
Standard generators of the Dempwolff group 25.L5(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 L5(2).
NB: There is just one class of involutions of 25.L5(2)
not in the normal 25 and it maps onto class 2A of L5(2).
A presentation of 25.L5(2) on its standard generators is given below.
< a, b | a2 = b5 = (ab)21 = [a, b2]4 = [a, b-2ab-2][a, b]3 = (ababab-2)2(abab-1ab)2(ab-1)2 = 1 >.
This presentation is available in Magma format as follows:
25L5(2) on a and b.
The representations of 25.L5(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) = 24.24.L3(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.