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:
The group is usually defined via the online ATLAS (within Magma), but for some groups which are not in the ATLAS, definitions have been used from the database built by Derek Holt; the input code temporarily uses a special intrinsic which can be found here (simply save that file and attach it in Magma first).
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.