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 A129520 Orders of symmetric groups associated with the exceptional groups G2, F4, E6, E7, E7.5, E8, E9 (or better? E11): A_3, S_3, A_4, S_5, "? ", A_5, S_5. 0
 3, 6, 24, 40, 60, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The calculation by hand based on dimensions of: Dim_Ex(i)-n(i)*Dim_Symm(i)=small_integer The groups E7.5 and E9 are better thought of as E7.6 and E11 when integer results are wanted. The "?" question mark group is a symmetrical group between s4 and A5 with dimension 40; it is not in any of the books I have or on the web as far as I can find by searching. REFERENCES Gareth Jones and David Singerman, Bull. London Math Soc. 28, (1996) pages 561-590 ( A_4, S_4, A_5 on p585) LINKS Table of n, a(n) for n=1..6. EXAMPLE 14-4*3=2 52-8*6=4 78-5*12=6 133-5*24=13 190-4.6*40=6 248-4*60=8 484-4*120=4 Example: DimEx(E7.6)/Dim_cartan=190/7.6=25 DimEx(E11)/Dim_cartan=484/11=44 which fit in the sequence of the traditional exceptional groups A118889 as:3, 7, 13, 13, 19, 25, 31,44 CROSSREFS Cf. A118889. Sequence in context: A101738 A083525 A106213 * A330300 A047167 A271428 Adjacent sequences: A129517 A129518 A129519 * A129521 A129522 A129523 KEYWORD nonn,uned,obsc AUTHOR Roger L. Bagula, May 28 2007 EXTENSIONS Partially edited by N. J. A. Sloane, May 15 2010 STATUS approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)