ATLAS: Symplectic group S_{6}(3)
Order = 4585351680 = 2^{9}.3^{9}.5.7.13.
Mult = 2.
Out = 2.
Standard generators of S6(3) are a and b where
a is in class 2A, b has order 5, ab has order 13
and abb has order 14.
Standard generators of the double cover 2.S6(3) are preimages A
and B where B has order 5 and AB has order 13.
Standard generators of S6(3):2 are c and d where c is in
class 2A, d is in class 4F, cd has order 20 and
cdd has order 8.
Standard generators of either 2.S6(3).2 are preimages C and D
where CDCDCDCDDCDDD has order 13.
WARNING: The standard generators in v2.0 for S6(3):2 and 2.S6(3).2 were defined on 27.06.00. The representations in v2.0 for S6(3):2 and 2.S6(3).2 are in these standard generators. There are [or were] no standard generators in v1 for S6(3):2 or 2.S6(3).2. The reprsentations of S6(3):2 and 2.S6(3).2 in v1 are NOT in standard generators as we have defined them above.
The representations of S_{6}(3) available are:

Permutations on 364 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 1120 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 3640 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 7371 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 13 over GF(4):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 13 over GF(25):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 13 over GF(7):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 2.S_{6}(3) available are:

Dimension 6 over GF(3)  the natural representation:
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of S_{6}(3):2 available are:

Permutations on 364 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 1120 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 3640 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Permutations on 7371 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 26 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 13 over GF(3):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 2.S_{6}(3):2 available are:

Permutations on 728 points:
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).

Dimension 6 over GF(3):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
The maximal subgroups of S_{6}(3) are as follows:

3^{1+4}:2.U_{4}(2),
with generators here.

3^{6}:L_{3}(3),
with generators here.

3^{1+4}:2.(S_{4} × A_{4}).

2.(A_{4} × U_{4}(2)),
with generators here.

2^{2+6}:3^{3}:S_{3},
with generators here.

L_{2}(27):3,
with generators here.

U_{3}(3):2 × 2,
with generators here.

L_{3}(3):2,
with generators here.

L_{2}(13),
with generators here.

L_{2}(13),
with generators here.

A_{5},
with generators here.
The maximal subgroups of S_{6}(3):2 are as follows:
Go to main ATLAS (version 2.0) page.
Go to classical groups page.
Go to old S6(3) page  ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 7th June 2000.
Last updated 02.08.05 by RAW.
Information checked to
Level 0 on 07.06.00 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.