A108755 Number of finite simple groups possessing an irreducible representation of dimension n.

0, 2, 1, 4, 4, 6, 4, 5, 7, 6, 5, 8, 8, 7, 6, 3, 4, 2, 6, 10, 6, 5, 4, 3, 7, 7, 8, 2, 6

Offset

2,2

Comments

The sequence starts at 2 because all finite simple groups have an irreducible representation of dimension 1 (namely the trivial representation).

Links

Table of n, a(n) for n=2..30.

G. Hiss and G. Malle, Low-dimensional representations of quasi-simple groups, LMS J. Comput. Math. 4 (2001) 22-63, corrigenda in same J. 5 (2002) 95-126.

Example

a(3)=2 because A_5 and L2(7) are the only finite simple groups to have irreducible representations of dimension 3.

Prog

(GAP) Simple := AllCharacterTableNames(IsSimple, true); list := List([1..16], x->0); for G in Simple do k := List(Irr(CharacterTable(G)), x->x[1]); for i in [1..16] do if i in k then list[i] := list[i] + 1; fi; od; od; # Note that we stop at 16 because currently GAP does not have the character table of A18 (which has a 17-dimensional representation)

Crossrefs

Sequence in context: A351168 A196082 A273724 * A093049 A326146 A081243

Adjacent sequences: A108752 A108753 A108754 * A108756 A108757 A108758

Keyword

nonn,more

Author

Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 23 2005

Status

approved