ATLAS: Tilman Schulz’s integral representations

Tilman Schulz's integral representations of sporadic groups. (Was supposed to include representatives of all complex representations of degree up to 250, but only a few are here.)

For the groups J1 and M11, representatives of all (isomorphism classes of) faithful Q-irreducible representations are given. For J2 only the representation corresponding to the degree 288, 300 and 336 characters are absent (these representations would have degrees 288, 300 and 672, even though all the characters are rational).
Note that the degree 336 character of J2 is a rare example of a character with rational character values and indicator + that cannot be realised over the rationals.


Group J1

Group J2

Group J3

Group M11

Group Th

Other content

This contains files to check (not prove) the material given here. For each group there is also an output file obtained by checking the representations for the said group.
GroupCheck fileOutput file

Version 2.0 created on 4th March 2009.
Last updated 04.03.09 by JNB.
R.A.Wilson, R.A.Parker, S.J.Nickerson and J.N.Bray.