Symplectic group S6(2)
Order = 1 451 520 = 29.34.5.7.
Mult = 2.
Out = 1.
Robert Wilson's ATLAS page for S6(2) is available here.
S6(2): Length 111, 2-generator, 7-relator.
< x, y | x2 = y7 = (xy)9 = (xy2)12 = [x, y]3 = [x, y2]2 = [x, y3]3 = 1 >
Remark: x and y are R.A.Wilson's standard generators for S6(2).
S6(2) x 2: Length 110, 7-generator, 28-relator.
< a, b, c, d, e, f, g | a2 = b2 = c2 = d2 = e2 = f2 = g2 = 1 = (ab)3 = [a, c] = [a, d] = [a, e] = [a, f] = [a, g] = (bc)3 = [b, d] = [b, e] = [b, f] = [b, g] = (cd)3 = [c, e] = [c, f] = (cg)3 = (de)3 = [d, f] = [d, g] = (ef)3 = [e, g] = [f, g] >
Remark: This is the Coxeter (diagram) group corresponding to the Weyl group of the exceptional Lie algebra of type E7.
Last updated 16th July, 1997
John N. Bray