A178780 -id:A178780 - cp's OEIS frontend

A178795 Expansion of the polynomial (x^15-1)(x^12-1)(x^10-1)(x^9-1)(x^7-1)(x^6-1)(x^4-1)*(x-1) in increasing powers of x.

1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 1, -2, 3, -1, -1, 3, -3, 1, 1, -4, 3, -1, -3, 4, -4, 1, 3, -5, 4, 0, -3, 6, -3, 0, 4, -5, 3, 1, -4, 4, -3, -1, 3, -4, 1, 1, -3, 3, -1, -1, 3, -2, 1, 1, -1, 1, 0, -1, 1, -1, 0, 0, -1, 1

Offset: 0

N. J. A. Sloane, Dec 26 2010

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

			With p=2 one gets the order of E_8(2): 337804753143634806261388190614085595079991692242467651576160959909068800000. - _Jean-François Alcover_, Aug 25 2022

R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.

Wikipedia, Lie group E8

Cf. A009968, A178779, A178780, A178781.

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

A008871 Order of universal Chevalley group E_6 (q), q = prime power.

Original entry on oeis.org

214841575522005575270400, 14515406695082926420056516790429286400, 85528710781342640103833619055142765466746880000, 3175144122737732284276405334472656250000000000000000000

Offset: 1

N. J. A. Sloane

nonn

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

Cf. A178780.

q^36*(q^2-1)*(q^5-1)*(q^6-1)*(q^8-1)*(q^9-1)*(q^12-1);

cp's OEIS Frontend

A178795 Expansion of the polynomial (x^15-1)(x^12-1)(x^10-1)(x^9-1)(x^7-1)(x^6-1)(x^4-1)*(x-1) in increasing powers of x.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

A008871 Order of universal Chevalley group E_6 (q), q = prime power.

Views

Author

Keywords

References

Crossrefs

Programs

Maple

cp's OEIS Frontend

A178795 Expansion of the polynomial (x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1) in increasing powers of x.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

A008871 Order of universal Chevalley group E_6 (q), q = prime power.

Views

Author

Keywords

References

Crossrefs

Programs

Maple

A178795 Expansion of the polynomial (x^15-1)(x^12-1)(x^10-1)(x^9-1)(x^7-1)(x^6-1)(x^4-1)*(x-1) in increasing powers of x.