ATLAS: Linear group L2(32)
Order = 32736.
Mult = 1.
Out = 5.
Standard generators
Standard generators of L2(32) are a
and b where
a has order 2, b has order 3
and ab is in class 31A/B/C/D/E. The last condition is
equivalent to saying that ab has order 31 and
ababb has order 11.
Standard generators of L2(32).5 are (for the moment at least)
c and d where
c has order 2, d has order 5,
cd, cdd, cdcdd, cdcdcdd each have order 15, and
cdcdcdcddcdcddcdd has order 11.
Presentations
Presentations for L_{2}(32) and L_{2}(32):5 in terms of their standard generators are given below.
< a, b | a^{2} = b^{3} = (ab)^{31} = (ab)^{4}(ab^{-1}abab^{-1})^{3}(ab)^{4}(ab^{-1})^{2} = 1 >.
< c, d | c^{2} = d^{5} = (cd)^{??} = ... = 1 >.
Representations
The representations of L2(32) available are
- a and
b as
permutations on 33 points.
- a and
b as
2 x 2 matrices over GF(32) - the natural representation.
The representations of L2(32).5 available are
- c and
d as
10 x 10 matrices over GF(2).
Maximal subgroups
The maximal subgroups of L2(32) are as follows.
The maximal subgroups of L2(32):5 are as follows.
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Last updated 07.10.96
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk