Finite Group Databasebeta

← Group #130366

Character table — Group #130366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244222244444444444448888888822444444488884444
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-111111111-111-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ9111111-1-1-1-1-1-111-1-1-1111111-1-1iiii−i−i−i−i-11-1-111-11-1ii−i−ii−ii−i
χ10111111-1-1-1-1-1-111-1-1-1111111-1-1iiii−i−i−i−i-1-111-1-11-11ii−i−i−ii−ii
χ11111111-1-1-1-1-1-111-1-1-1111111-1-1−i−i−i−iiiii-11-1-111-11-1−i−iii−ii−ii
χ12111111-1-1-1-1-1-111-1-1-1111111-1-1−i−i−i−iiiii-1-111-1-11-11−i−iiii−ii−i
χ13111111-1-1-1-1-1-111-1-1-111-1-1-1-111iiii−i−i−i−i11-11-11-1-11−i−iiii−i−ii
χ14111111-1-1-1-1-1-111-1-1-111-1-1-1-111iiii−i−i−i−i1-11-11-111-1−i−iii−iii−i
χ15111111-1-1-1-1-1-111-1-1-111-1-1-1-111−i−i−i−iiiii11-11-11-1-11ii−i−i−iii−i
χ16111111-1-1-1-1-1-111-1-1-111-1-1-1-111−i−i−i−iiiii1-11-11-111-1ii−i−ii−i−ii
χ17222222222-22-2-2-22-2-22-2000000000000000002200-2-200000000
χ18222222222-22-2-2-22-2-22-200000000000000000-2-2002200000000
χ1922222222-22-22-2-22-2-2-220000000000000002200-2-20000000000
χ2022222222-22-22-2-22-2-2-22000000000000000-2-200220000000000
χ2122222222-2-2-2-222222-2-222-2-2-2-20000000020000000000000000
χ2222222222-2-2-2-222222-2-2-2-2222200000000-20000000000000000
χ23222222-2-2222222-2-2-2-2-222-2-22200000000-20000000000000000
χ24222222-2-2222222-2-2-2-2-2-2-222-2-20000000020000000000000000
χ25222222-2-22-22-2-2-2-222-220000000000000002-200-220000000000
χ26222222-2-22-22-2-2-2-222-22000000000000000-22002-20000000000
χ27222222-2-2-22-22-2-2-2222-2000000000000000002-2002-200000000
χ28222222-2-2-22-22-2-2-2222-200000000000000000-2200-2200000000
χ2922-2-22-2002-2-222-2000002i−2i002i−2i22−2−222−2−2000000000i2−i2i2−i20000
χ3022-2-22-2002-2-222-2000002i−2i002i−2i−2−222−2−222000000000−i2i2−i2i20000
χ3122-2-22-2002-2-222-200000−2i2i00−2i2i22−2−222−2−2000000000−i2i2−i2i20000
χ3222-2-22-2002-2-222-200000−2i2i00−2i2i−2−222−2−222000000000i2−i2i2−i20000
χ3322-2-22-200-222-22-2000002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2000000000−222−20000
χ3422-2-22-200-222-22-2000002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i20000000002−2−220000
χ3522-2-22-200-222-22-200000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i20000000002−2−220000
χ3622-2-22-200-222-22-200000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2000000000−222−20000
χ374444-4-444000000-400000000002-22-22-22-200000000000000000
χ384444-4-444000000-40000000000-22-22-22-2200000000000000000
χ394444-4-4-4-4000000400000000002i−2i2i−2i−2i2i−2i2i00000000000000000
χ404444-4-4-4-400000040000000000−2i2i−2i2i2i−2i2i−2i00000000000000000
χ4144-4-44-40044-4-4-44000000000000000000000000000000000000
χ4244-4-44-400-4-444-44000000000000000000000000000000000000
χ4344-4-4-440000000004i−4i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000
χ4444-4-4-440000000004i−4i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000
χ4544-4-4-44000000000−4i4i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000
χ4644-4-4-44000000000−4i4i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000
χ478-88-8008i−8i000000000000000000000000000000000000000000
χ488-88-800−8i8i000000000000000000000000000000000000000000
χ498-8-88000000000000000004-4000000000000000000000000000
χ508-8-8800000000000000000-44000000000000000000000000000

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