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A108755
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Number of finite simple groups possessing an irreducible representation of dimension n.
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0
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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
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2,2
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COMMENTS
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The sequence starts at 2 because all finite simple groups have an irreducible representation of dimension 1 (namely the trivial representation).
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LINKS
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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.
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EXAMPLE
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a(3)=2 because A_5 and L2(7) are the only finite simple groups to have irreducible representations of dimension 3.
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PROG
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(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)
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CROSSREFS
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Sequence in context: A351168 A196082 A273724 * A093049 A326146 A081243
Adjacent sequences: A108752 A108753 A108754 * A108756 A108757 A108758
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KEYWORD
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nonn,more
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AUTHOR
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Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 23 2005
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STATUS
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approved
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