ATLAS: Non­split extension 53.L3(5)

Order = 46500000 =
Mult = 1.
Out = 1.
The page for the image L3(5) is available here.

The following information is available for 53.L3(5):

Standard generators

Type I standard generators for 53.L3(5) are a and b where a has order 3, b is in class 5B, ab has order 20, abb has order 31, ababbbaabbb has order 4 and ababaababb has order 3. These generators map onto Type I standard generators of L3(5).
Type II standard generators for 53.L3(5) are x and y where x has order 2, y has order 3, xy has order 31, xyxy2 has order 25, (xy)5(xy2)4 has order 2 and (xyxyxy2xy2)2xyxy2 has order 3. These generators map onto Type II standard generators of L3(5).

NB: All elements of order 5 of 53.L3(5) not in the normal 53 map onto class 5A of L3(5).
NB: Class 5B is the unique class with centraliser order 2500.

We may obtain a conjugate of (a, b) as: a' = yxyx, b' = ((xyxyxyy)2xyy)4.


A presentation of 53.L3(5) on its standard generators is given below.

< x, y | x2 = y3 = (xy)31 = ((xy)5(xy-1)4)2 = [x, yxy(xy-1)3xyxy(xy-1)3xyxy] = [x, yxy]10 = (xy)6xy-1xy(xyxy-1)3xy-1xy(xy-1)5xyxy-1(xy)5xy-1xy-1 = 1 >.

This presentation is available in Magma format as follows: 53L3(5) on x and y.


The representations of 53.L3(5) available are:
Main ATLAS page Go to main ATLAS (version 2.0) page.
Miscellaneous groups page Go to miscellaneous groups page.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 13th July 1999.
Last updated 08.02.02 by JNB.
Information checked to Level 0 on 20.07.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.