cp's OEIS Frontend

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.

%I A129520 #5 May 01 2013 21:08:56
%S A129520 3,6,24,40,60,120
%N 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.
%C A129520 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.
%D A129520 Gareth Jones and David Singerman, Bull. London Math Soc. 28, (1996) pages 561-590 ( A_4, S_4, A_5 on p585)
%e A129520 14-4*3=2
%e A129520 52-8*6=4
%e A129520 78-5*12=6
%e A129520 133-5*24=13
%e A129520 190-4.6*40=6
%e A129520 248-4*60=8
%e A129520 484-4*120=4
%e A129520 Example:
%e A129520 DimEx(E7.6)/Dim_cartan=190/7.6=25
%e A129520 DimEx(E11)/Dim_cartan=484/11=44
%e A129520 which fit in the sequence of the traditional exceptional groups A118889
%e A129520 as:3, 7, 13, 13, 19, 25, 31,44
%Y A129520 Cf. A118889.
%K A129520 nonn,uned,obsc
%O A129520 1,1
%A A129520 _Roger L. Bagula_, May 28 2007
%E A129520 Partially edited by _N. J. A. Sloane_, May 15 2010