ATLAS: Suzuki group Sz(32)
Order =32537600.
Mult = 1.
Out = 5.
Standard generators
Standard generators of Sz(32) are a
and b where
a has order 2, b has order 4,
ab has order 5,
ababb has order 25, and
abababbababbabb has order 25.
Standard generators of Sz(32):5 are
c
and d where
c has order 2, d has order 5,
cd has order 5,
cdcdddd has order 5,
cddcddd has order 31, and
cdcddcddd has order 10.
Representations
The representations of Sz(32) available are
- a and
b as
4 x 4 matrices over GF(32) - the natural representation.
- a and
b as
124 x 124 matrices over GF(5).
- a and
b as
124 x 124 matrices over GF(41).
- a and
b as
permutations on 1025 points.
- a and
b as
permutations on 198400 points.
The representations of Sz(32):5 available are as follows.
- c and
d as
20 x 20 matrices over GF(2).
- c and
d as
124 x 124 matrices over GF(5).
- c and
d as
248 x 248 matrices over GF(5) - exhibiting the inclusion in E8(5).
The given basis is a Chevalley basis, and
the Lie algebra coproduct is here
as a 248 x 248^{2} matrix.
- c and
d as
124 x 124 matrices over GF(41).
- c and
d as
permutations on 1025 points.
Maximal subgroups
The maximal subgroups of Sz(32) are
The maximal subgroups of Sz(32):5 are
- Sz(32)
- 2^5+5:31:5
- 41:20
- 25:20
- 31:10
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Last updated 29.10.99
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk