ATLAS: Linear group L2(32)
Order = 32736.
Mult = 1.
Out = 5.
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 for L2(32) and L2(32):5 in terms of their standard generators are given below.
< a, b | a2 = b3 = (ab)31 = (ab)4(ab-1abab-1)3(ab)4(ab-1)2 = 1 >.
< c, d | c2 = d5 = (cd)?? = ... = 1 >.
The representations of L2(32) available are
The representations of L2(32).5 available are
- a and
permutations on 33 points.
- a and
2 x 2 matrices over GF(32) - the natural representation.
- c and
10 x 10 matrices over GF(2).
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