

A108755


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


0



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
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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, Lowdimensional representations of quasisimple groups, LMS J. Comput. Math. 4 (2001) 2263, corrigenda in same J. 5 (2002) 95126.


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 17dimensional 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



