ATLAS: Exceptional group 2E6(2)
Order = 76532479683774853939200 = 236.39.52.72.11.13.17.19.
Mult = 22 × 3.
Out = S3.
Standard generators of 2E6(2) are a and b
where a is in class 2B, b is in class 3C,
ab has order 19 and abababb has order 33.
Standard generators of the double cover 2.2E6(2) are
preimages A and B where B has order 3, AB has
order 19 and ABABABB has order 33.
Standard generators of the triple cover 3.2E6(2) are
preimages A and B where A has order 2 and AB
has order 19.
Standard generators of 2E6(2):2 are e and
f where e is in class 2D, f is in class 8R,
ef has order 19, and efeff has order 30.
Standard generators of 3.2E6(2):2 are preimages
E and F where EF has order 19.
Standard generators of 2.2E6(2):2 are preimages
E and F where EF has order 19.
Standard generators for the other groups below are not defined.
An automorphism of order 3 of 2E6(2) may be obtained by mapping
(a, b) to
((ab)^-2bab, (abb)^-6b(abb)^6).
An automorphism of order 2 of 2E6(2) may be obtained by mapping
(a, b) to
(a, (abb)^-9b(abb)^9).
2E6(2) and covers
- The representations of 2E6(2) available are:
-
Dimension 78 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
-
Dimension 1705 (structure 1702.(1+1+1)) over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
- The representation of 2.2E6(2) available is:
-
Dimension 1704 over GF(2):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- The representation of 22.2E6(2) available is:
-
Dimension 1706 over GF(2):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
- The representation of 3.2E6(2) available is:
-
Dimension 27 over GF(4):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
2E6(2):2 and covers
- The representation of 2E6(2):2 available is:
-
Dimension 78 over GF(2):
e and
f (Meataxe),
e and
f (Meataxe binary),
e and
f (GAP).
-
Dimension 1938 over GF(3):
e and
f (Meataxe),
e and
f (Meataxe binary),
e and
f (GAP).
- The representation of 3.2E6(2):2 available is:
-
Dimension 54 over GF(2):
E and
F (Meataxe),
E and
F (Meataxe binary),
E and
F (GAP).
- The representations of 2.2E6(2):2 available are:
-
Dimension 1705 over GF(2):
E and
F (Meataxe),
E and
F (Meataxe binary),
E and
F (GAP).
-
Dimension 2432 over GF(3):
E and
F (Meataxe),
E and
F (Meataxe binary),
E and
F (GAP).
2E6(2):3 and covers
- The representation of 2E6(2):3 available is:
-
Dimension 78 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
- The representation of 3.2E6(2).3 available is:
-
Dimension 27 over GF(4):
C' and
D' (Meataxe),
C' and
D' (Meataxe binary),
C' and
D' (GAP).
2E6(2):S3 and covers
- The representation of 2E6(2):S3 available is:
-
Dimension 78 over GF(2):
g and
h (Meataxe),
g and
h (Meataxe binary),
g and
h (GAP).
- The representation of 3.2E6(2):S3 available is:
-
Dimension 54 over GF(2):
G' and
H' (Meataxe),
G' and
H' (Meataxe binary),
G' and
H' (GAP).
The maximal subgroups of 2E6(2) include:
The maximal subgroups of 2E6(2):2 include:
Go to main ATLAS (version 2.0) page.
Go to exceptional groups page.
Go to old 2E6(2) page - ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 26th April 2000.
Last updated 06.01.04 by RAW.
Information checked to
Level 0 on 23.05.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.