ATLAS: Rudvalis group Ru

Order = 145926144000 =
Mult = 2.
Out = 1.

The following information is available for Ru:

Standard generators

Standard generators of the Rudvalis group Ru are a and b where a is in class 2B, b is in class 4A and ab has order 13.
Standard generators of the double cover 2.Ru are preimages A and B where B is in class +4A and AB has order 13. An equivalent condition to B being in class +4A is that ABABB has order 29.

Black box algorithms

Finding generators

To find standard generators for Ru: This algorithm is available in computer readable format: finder for Ru.

Checking generators

To check that elements x and y of Ru are standard generators:

This algorithm is available in computer readable format: checker for Ru.


The representations of Ru available are: The representations of 2.Ru available are:

Maximal subgroups

The maximal subgroups of Ru are as follows. Words for generators of maximal subgroups provided by Peter Walsh. Some [shorter] words that have subsequently been computed.

Conjugacy class representatives

The following conjugacy class representatives have been computed by Peter Walsh. Click here for program to compute them. The choice of classes among algebraic conjugates is arbitrary, consistent with the ordinary ATLAS. The given choice has been used by Frank Röhr in calculating the 13­ and 29­modular characters, but may not be consistent with other GAP tables. (Actually, we have replaced some of Peter's class representatives by shorter words while retaining his definitions of the classes. Version 1 contains Peter's class list.) A different set of generators for the maximal cyclic subgroups (up to conjugacy) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements. Problems of algebraic conjugacy: all classes except 14ABC and 20BC are compatible with the other class list; 14ABC and 20BC are not dealt with in this version.
Main ATLAS page Go to main ATLAS (version 2.0) page.
Sporadic groups page Go to sporadic groups page.
Old Ru page Go to old Ru page - ATLAS version 1.
ftp access Anonymous ftp access is also available. See here for details.

Version 2.0 created on 21st May 1999.
Last updated 10.1.05 by SJN.
Information checked to Level 0 on 21.05.99 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.