Finite Group Databasebeta

← Group #139708

Character table — Group #139708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222222448888888888888888888881616161616161616323232323232
order12222244444422222444444448888888824448888888888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-111
χ8111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ9111111-1-1-1-11111-111-1-111-1-1-1-1ii−i−iii−i−i1-1-11i−ii−i1-1i−ii−i
χ10111111-1-1-1-11111-111-1-111-1-1-1-1ii−i−iii−i−i-111-1i−ii−i-11−ii−ii
χ11111111-1-1-1-11111-111-1-111-1-1-1-1−i−iii−i−iii1-1-11−ii−ii1-1−ii−ii
χ12111111-1-1-1-11111-111-1-111-1-1-1-1−i−iii−i−iii-111-1−ii−ii-11i−ii−i
χ13111111-1-1-1-11111-1-1-111-1-111-1-1ii−i−i−i−iii1-1-11i−i−ii-11i−i−ii
χ14111111-1-1-1-11111-1-1-111-1-111-1-1ii−i−i−i−iii-111-1i−i−ii1-1−iii−i
χ15111111-1-1-1-11111-1-1-111-1-111-1-1−i−iiiii−i−i1-1-11−iii−i-11−iii−i
χ16111111-1-1-1-11111-1-1-111-1-111-1-1−i−iiiii−i−i-111-1−iii−i1-1i−i−ii
χ17222222222222-2-222222-2-2-2-2-2-20000000000000000000000
χ18222222222222-2-22-2-2-2-22222-2-20000000000000000000000
χ192222222222-2-22-2-2000000002-200002222000000-2-2000000
χ202222222222-2-22-2-2000000002-20000-2-2-2-200000022000000
χ212222222222-2-2-22-200000000-22222200000000-2-200000000
χ222222222222-2-2-22-200000000-22-2-2-2-2000000002200000000
χ23222222-2-2-2-222-2-2-222-2-2-2-222220000000000000000000000
χ24222222-2-2-2-222-2-2-2-2-22222-2-2220000000000000000000000
χ25222222-2-2-2-2-2-22-2200000000-2200002i2i−2i−2i000000−2i2i000000
χ26222222-2-2-2-2-2-22-2200000000-220000−2i−2i2i2i0000002i−2i000000
χ27222222-2-2-2-2-2-2-222000000002-22i2i−2i−2i00000000−2i2i00000000
χ28222222-2-2-2-2-2-2-222000000002-2−2i−2i2i2i000000002i−2i00000000
χ294444-4-444-4-40000000000000000000000022-2-20000000000
χ304444-4-444-4-400000000000000000000000-2-2220000000000
χ314444-4-4-4-444000000000000000000000002-22-20000000000
χ324444-4-4-4-44400000000000000000000000-22-220000000000
χ3344-4-4004i−4i000000000002-22i−2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000
χ3444-4-4004i−4i000000000002-22i−2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000
χ3544-4-4004i−4i00000000000-22−2i2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000000000
χ3644-4-4004i−4i00000000000-22−2i2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000000000
χ3744-4-400−4i4i000000000002-2−2i2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000
χ3844-4-400−4i4i000000000002-2−2i2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000
χ3944-4-400−4i4i00000000000-222i−2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000000000
χ4044-4-400−4i4i00000000000-222i−2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000000000
χ414-4-44-4400004-4000004-40000000000000000000000000000
χ424-4-44-4400004-400000-440000000000000000000000000000
χ434-4-44-440000-440004-4000000000000000000000000000000
χ444-4-44-440000-44000-44000000000000000000000000000000
χ458-88-800008i−8i0000000000000000000000000000000000000
χ468-88-80000−8i8i0000000000000000000000000000000000000
χ478-8-888-800000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.