ATLAS: Linear group L3(5)

Order = 372000 =
Mult = 1.
Out = 2.
The page for the group 53.L3(5) (non-split extension) is available here.

The following information is available for L3(5):

Standard generators

Type I standard generators of L3(5) are a and b where a has order 3, b is in class 5A and ab has order 20.
Type II standard generators of L3(5) are x and y where x has order 2, y has order 3, xy has order 31 and xyxyy has order 5.

Standard generators of L3(5):2 are c and d where c is in class 2B, d is in class 4D and cd has order 12.

We may obtain .. as x = ((ab)10)babb, y = a, and a' = a = y, b' = ((xyyxyyxyxy)4)yxyyx. The composition of these two maps (either way round) is equivalent to conjugating the generators by an outer element, o say [which is the same either way round], in class 6B, where o-2 = a = y.


Presentations for L3(5) and L3(5):2 on their standard generators are given below.

< a, b | a3 = b5 = aba-1baba-1b2ab-2a-1b2 = abab-2(a-1b2a-1b-2)3 = 1 >.

< x, y | x2 = y3 = (xy)31 = [x, y]5 = ((xy)5(xy-1)4)2 = 1 >.

< c, d | c2 = d4 = (cd)12 = (cdcd2cd2)3 = [d2, cdc]3 = [c, dcdcd-1cdcdcd-1cdcd] = 1 >.

These presentations are available in Magma format as follows: L3(5) on a and b, L3(5) on x and y and L3(5):2 on c and d.


The representations of L3(5) available are: The representations of L3(5):2 available are:

Maximal subgroups

The maximal subgroups of L3(5) are as follows. The maximal subgroups of L3(5):2 are as follows.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.
Old L3(5) page Go to old L3(5) page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 28th July 1999.
Last updated 04.02.02 by JNB.
Information checked to Level 0 on 30.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.