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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 * A047167 A271428 A148649

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 May 27 06:24 EDT 2019. Contains 323599 sequences. (Running on oeis4.)