ATLAS: Suzuki group Sz(32)
Order = 32537600 = 2^{10}.5^{2}.31.41.
Mult = 1.
Out = 5.
The following information is available for Sz(32):
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.
The representations of Sz(32) available are:

Dimension 4 over GF(32)  the natural representation:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 124 over GF(5):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 124 over GF(41):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 1025 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Permutations on 198400 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of Sz(32):5 available are:

Dimension 20 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 124 over GF(5):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 124 over GF(41):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 248 over GF(5):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
 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.

Permutations on 1025 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
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.
A set of generators for the maximal cyclic subgroups of
Sz(32) can be obtained
by running this program on the standard
generators. All conjugacy classes can therefore be obtained as suitable
powers of these elements.
A set of generators for the maximal cyclic subgroups of
Sz(32):5 can be obtained
by running this program on the standard
generators. All conjugacy classes can therefore be obtained as suitable
powers of these elements.
Go to main ATLAS (version 2.0) page.
Go to sporadic groups page.
Go to old Sz(32) page  ATLAS version 1.
Anonymous ftp access is also available.
See here for details.
Version 2.0 created on 28th April 2000.
Last updated 18.07.00 by JNB.
Information checked to
Level 0 on 28.04.00 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.