ATLAS: Nonsplit extension 2^{4}.A_{8} = 2^{4}.L_{4}(2)
Order = 322560 = 2^{10}.3^{2}.5.7.
Mult = 2.
Out = 1.
The page for the image A_{8} = L_{4}(2) is available
here.
The following information is available for 2^{4}.A_{8}:
Standard generators of 2^{4}.A_{8} are a and b
where a is in class 3A, b has order 7, ab has order 6,
[a, b] has order 2 and abab^{2}ab^{5} has order
6. An equivalent condition to [a, b] having order 2 is that abbb
has order 12. These generators map onto standard generators of A_{8}.
Standard generators of the double cover 2^{4}.2A_{8} are
preimages A and B where A has order 3 and B has
order 7. These generators map onto standard generators of 2A_{8}.
NB: Class 3A is the class of elements of order 3 with centraliser 3 ×
A_{5}, and maps onto Class 3A of A_{8}.
A presentation of 2^{4}.A_{8} on its standard generators is given below.
< a, b  a^{3} = b^{7} = (ab)^{6} = [a, b]^{2} = abab^{2}a^{1}bab^{2}ab^{3}ab^{3}ab^{3} = 1 >.
This presentation is available in Magma format as follows:
24A8 on a and b.
The representations of 2^{4}.A_{8} available are:

Permutations on 30 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 128 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 11 over GF(2)  uniserial module 4.6.1:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 11 over GF(2)  uniserial module 1.6.4:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15 over GF(3):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 15 over Z  monomial:
a and
b (Meataxe),
a and b (GAP),
a and b (Magma).
Go to main ATLAS (version 2.0) page.
Go to miscellaneous groups page.
There is no old 24A8 page (not even on the A8 page) in the ATLAS version 1.
Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 created on 24th July 1999.
Last updated 24.07.99 by JNB.
Information checked to
Level 0 on 24.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.