Ordinary Representations Database

Allan Steel (January 2012)

This page has a small selection from the database of over 1000 absolutely irreducible ordinary representations of finite groups which I constructed in 2010-2011.

The database includes the following absolutely irreducible ordinary representations (always realized over a minimal field):

The database was built by my implementation in Magma of the algorithms for constructing representations which are in my PhD thesis (Construction of Ordinary Irreducible Representations of Finite Groups).

The following selection picks out some examples which are discussed in my thesis, plus a few others of interest. Most of these representations have never been constructed before (at least over a minimal field and with small entries), and so this fills very many gaps in characteristic zero at the Online ATLAS of Finite Group Representations.

The selection of representations given here will be expanded greatly!


Information on the table:


Degree Group CFD SI Time Notes
12 6.Suz * 2 1 66 
18 3.J3 * 4 1 7.5  
35 Sz(8) 3 1 0.8  
36 6.A7 2 1 2.9  
36 2.L2(71) 2 1 11 
40 2.Sz(8) * 3 1 3.6  
51 U4(4) * 4 1 26 
51 He * 2 1 18 
56 J1 * 2 1 0.7 
60 12_2.L3(4) 8 1 139 
66 6.M22 * 4 1 6.2 
66 3.Suz * 2 1 23 
70 J2 2 1 1.7 
75 U3(4) 4 1 4.9 
80 4_1.L3(4) 4 1 6.8 
80 4_2.L3(4) 4 1 17.6 
84 L2(83) 20 1 50 
85 J3 * 2 1 50 
96 L3(5) 10 1 12 
120 12.M22 * 8 1 309 
121 S10(3) * 2 1 1111 
122 2.S10(3) * 2 1 2334 
126 3.McL 4 1 72 
128 2.A16 * 1 1 228 
128 2.A17 * 2 1 3165 
133 HN * 2 1 16 
143 Suz * 1 1 13 
157 U3(13) 6 1 104 
170 U9(2) * 1 2 135 
171 3.U9(2) * 2 1 110 Irreducible extension of J3 (NF deg 2) representation
171 S6(7) * 2 1 334 
171 3.J3 2 1 41 
171 3.J3 4 1 860 
172 2.S6(7) * 2 1 139 
189 3.G2(3) 4 1 97 
204 U5(4) * 1 2 57 
205 5.U5(4) * 4 1 467 
208 2.S4(5) * 2 2 33 
216 12_1.U4(3) 4 1 293 
216 12_2.U4(3) 4 1 179 
220 2.Suz * 1 2 79 
221 U4(4) 2 1 38 
240 U3(16) * 1 2 108 0.9MB
241 U3(16) 16 1 1.8h 6.6MB
248 Th * 1 1 110 
273 3.U3(17) * 6 1 1333 
276 Co1 * 1 1 18 
342 3.O'N * 4 1 16.2h 3.5MB
351 3.Fi22 * 2 1 2745 3.4MB
352 2.Fi22 * 1 1 85 0.9MB
378 Ru * 2 1 31 1.5MB
760 HN 1 1 359 1.6MB gzipped file (6.4MB uncompressed)
782 Fi23 * 1 1 596 1.0MB gzipped file (4.2MB uncompressed)
783 3.Fi24' * 2 1 2.2h 2.1MB gzipped file (21MB uncompressed)
1333 J4 * 2 1 1354 2.3MB gzipped file (28MB uncompressed)
1728 6.Fi22 * 2 1 47.8h 41MB gzipped file (130MB uncompressed)
2480 Ly * 2 1 20.7h 21MB gzipped file (135MB uncompressed)
4371 B * 1 1 39.6h 39MB gzipped file (230MB uncompressed)

Minimal-degree representations of the Fischer group Fi24 (degree 8671 over Q) and the O'Nan group O'N (degree 10944 over Q) have also been constructed, but take a lot of space! I will eventually make them available, when I have developed a suitable compressed format.