ATLAS: Symplectic group S6(3)
Order = 4585351680.
Mult = 2.
Out = 2.
Standard generators
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 2S6(3) are pre-images
A
and B where B has order 5
and AB has order 13.
Standard generators of S6(3).2 are not defined.
Representation
The representations of S6(3) available are
- a and
b as
13 x 13 matrices over GF(4).
- a and
b as
permutations on 364 points.
- a and
b as
permutations on 1120 points.
- a and
b as
permutations on 3640 points.
- a and
b as
permutations on 7371 points.
The representations of S6(3):2 available are
- c and
d as
26 x 26 matrices over GF(2).
- c and
d as
13 x 13 matrices over GF(3).
- c and
d as
permutations on 364 points.
- c and
d as
permutations on 1120 points - this representation appears to be broken [it is the same as p3640].
- c and
d as
permutations on 3640 points.
- c and
d as
permutations on 7371 points.
The representation of 2.S6(3) available is
- A and
B as
6 x 6 matrices over GF(3) - the natural representation.
The representation of 2.S6(3):2 available is
- C and
D as
6 x 6 matrices over GF(3) - the natural representation.
- C and
D as
permutations on 728 points.
Maximal subgroups
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Last updated 06.07.00
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk