Finite Group Databasebeta

← Group #150604

Character table — Group #150604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size1122244448888888881616323232323232323232323232
order122442444244888888482444888816161616
χ111111111111111111111111111111111
χ21111111111111111111111-1-111-1-1-1-1-1-1
χ311111111111111111111-1-111-1-111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-11111
χ5111111111-11-11111-1-1-1-111i−i-1-1i−iii−i−i
χ6111111111-11-11111-1-1-1-111−ii-1-1−ii−i−iii
χ7111111111-11-11111-1-1-1-1-1-1i−i11i−i−i−iii
χ8111111111-11-11111-1-1-1-1-1-1−ii11−iiii−i−i
χ9111111-1-111-1111-1-111-1-11-1111-1-1-11-11-1
χ10111111-1-111-1111-1-111-1-11-1-1-11-111-11-11
χ11111111-1-111-1111-1-111-1-1-1111-11-1-1-11-11
χ12111111-1-111-1111-1-111-1-1-11-1-1-11111-11-1
χ13111111-1-11-1-1-111-1-1-1-1111-1i−i-11−iii−i−ii
χ14111111-1-11-1-1-111-1-1-1-1111-1−ii-11i−i−iii−i
χ15111111-1-11-1-1-111-1-1-1-111-11i−i1-1−ii−iii−i
χ16111111-1-11-1-1-111-1-1-1-111-11−ii1-1i−ii−i−ii
χ17222222222222-2-2-2-2-2-22-2000000000000
χ18222222222-22-2-2-2-2-222-22000000000000
χ19222222-2-222-22-2-222-2-2-22000000000000
χ20222222-2-22-2-2-2-2-222222-2000000000000
χ2144444-444-40-4000000000000000000000
χ2244444-4-4-4-404000000000000000000000
χ23444-4-4400-400000004i−4i00000000000000
χ24444-4-4400-40000000−4i4i00000000000000
χ25444-4-4-400440-400000000000000000000
χ26444-4-4-4004-40400000000000000000000
χ2788-88-8000000000000000000000000000
χ2888-8-88000000000000000000000000000
χ298-800004i−4i000022−222i2−2i20000000000000000
χ308-800004i−4i0000−2222−2i22i20000000000000000
χ318-80000−4i4i000022−22−2i22i20000000000000000
χ328-80000−4i4i0000−22222i2−2i20000000000000000

Here i is the imaginary unit (i² = −1).