OFFSET
0,13
COMMENTS
q^120*(q^30-1)*(q^24-1)*(q^20-1)*(q^18-1)*(q^14-1)*(q^12-1)*(q^8-1)*(q^2-1) is the order of the simple group E_8(q), if q is a prime power.
If f(x) is the x-polynomial and g(q) the q-polynomial, then g(q) = q^120*f(q^2). - Jean-François Alcover, Aug 25 2022
REFERENCES
R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.
LINKS
Wikipedia, Lie group E8
EXAMPLE
With p=2 one gets the order of E_8(2): 337804753143634806261388190614085595079991692242467651576160959909068800000. - Jean-François Alcover, Aug 25 2022
PROG
(PARI) Vec((x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1)) \\ Michel Marcus, Aug 25 2022
CROSSREFS
KEYWORD
sign,fini,full
AUTHOR
N. J. A. Sloane, Dec 26 2010
STATUS
approved