Finite Group Databasebeta

← Group #139607

Character table — Group #139607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size111122222244444488888888888888816161616161616161616323232323232
order12222244444444444444444888888884444448888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-111-1-1
χ61111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-11111-111-111-1-111-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-1-1-11-1-11-1-111-111-1-1ii−i−iii−i−i11-1-11-1i−ii−i1-1i−ii−i
χ10111111-1-1-1-11-1-11-1-111-111-1-1ii−i−iii−i−i1-11-1-11i−ii−i-11−ii−ii
χ11111111-1-1-1-11-1-11-1-111-111-1-1−i−iii−i−iii11-1-11-1−ii−ii1-1−ii−ii
χ12111111-1-1-1-11-1-11-1-111-111-1-1−i−iii−i−iii1-11-1-11−ii−ii-11i−ii−i
χ13111111-1-1-1-11-1-11-1-111-1-1-111ii−i−i−i−iii-11-111-1i−i−ii-11i−i−ii
χ14111111-1-1-1-11-1-11-1-111-1-1-111ii−i−i−i−iii-1-111-11i−i−ii1-1−iii−i
χ15111111-1-1-1-11-1-11-1-111-1-1-111−i−iiiii−i−i-11-111-1−iii−i-11−iii−i
χ16111111-1-1-1-11-1-11-1-111-1-1-111−i−iiiii−i−i-1-111-11−iii−i1-1i−i−ii
χ1722222222222-2-22-2-2-2-22222200000000-200-2000000000000
χ1822222222222-2-22-2-2-2-22-2-2-2-2000000002002000000000000
χ192222222222-22-2-22-22-2-200000000222200000000-2-2000000
χ202222222222-22-2-22-22-2-200000000-2-2-2-20000000022000000
χ212222222222-2-22-2-22-22-2000022220000000000-2-200000000
χ222222222222-2-22-2-22-22-20000-2-2-2-200000000002200000000
χ23222222-2-2-2-2222222-2-2-222-2-200000000-2002000000000000
χ24222222-2-2-2-2222222-2-2-2-2-22200000000200-2000000000000
χ25222222-2-2-2-2-22-2-22-2-22200002i2i−2i−2i0000000000−2i2i00000000
χ26222222-2-2-2-2-22-2-22-2-2220000−2i−2i2i2i00000000002i−2i00000000
χ27222222-2-2-2-2-2-22-2-222-22000000002i2i−2i−2i00000000−2i2i000000
χ28222222-2-2-2-2-2-22-2-222-2200000000−2i−2i2i2i000000002i−2i000000
χ294444-4-444-4-400000000000000000000002-20-220000000000
χ304444-4-444-4-40000000000000000000000-2202-20000000000
χ314444-4-4-4-4440000000000000000000000220-2-20000000000
χ324444-4-4-4-4440000000000000000000000-2-20220000000000
χ3344-4-44-4000044-4-4-440000000000000000000000000000000
χ3444-4-44-400004-44-44-40000000000000000000000000000000
χ3544-4-44-40000-4444-4-40000000000000000000000000000000
χ3644-4-44-40000-4-4-44440000000000000000000000000000000
χ374-4-44004i−4i000000000002i−2i2-22ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ384-4-44004i−4i000000000002i−2i2-2−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ394-4-44004i−4i00000000000−2i2i-222ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ404-4-44004i−4i00000000000−2i2i-22−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ414-4-4400−4i4i000000000002i−2i-222ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ30000000000000000
χ424-4-4400−4i4i000000000002i−2i-22−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ434-4-4400−4i4i00000000000−2i2i2-22ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ444-4-4400−4i4i00000000000−2i2i2-2−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000
χ4588-8-8-8800000000000000000000000000000000000000000
χ468-88-800008-80000000000000000000000000000000000000
χ478-88-80000-880000000000000000000000000000000000000

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