Unitary group U₄(2)
Symplectic group S₄(3)

Order = 25 920 = 2⁶.3².5.
Mult = 2.
Out = 2.

Robert Wilson's ATLAS page for U₄(2) is available here.

U₄(2): Length 46, 2-generator, 5-relator.

< x, y | x³ = y⁵ = (xy)⁹ = [x, y]² = (xy^-2xy²)² = 1 >

U₄(2):2: Length 82, 2-generator, 21-relator.

< a, b, c, d, e, f | a² = b² = c² = d² = e² = f² = 1 = (ab)³ = [a, c] = [a, d] = [a, e] = [a, f] = (bc)³ = [b, d] = [b, e] = [b, f] = (cd)³ = [c, e] = (cf)³ = (de)³ = [d, f] = [e, f] >

Remark: This is the Coxeter (diagram) group corresponding to the Weyl group of the exceptional Lie algebra of type E₆.

U₄(2) x 5: Length 28, 2-generator, 4-relator.

< x, y | x³ = y⁵ = [x, y]² = (xy^-2xy²)² = 1 >

Last updated 16^th July, 1997

John N. Bray

Unitary group U4(2) Symplectic group S4(3)

U4(2): Length 46, 2-generator, 5-relator.

U4(2):2: Length 82, 2-generator, 21-relator.

U4(2) x 5: Length 28, 2-generator, 4-relator.

Unitary group U₄(2)
Symplectic group S₄(3)

U₄(2): Length 46, 2-generator, 5-relator.

U₄(2):2: Length 82, 2-generator, 21-relator.

U₄(2) x 5: Length 28, 2-generator, 4-relator.