Finite Group Databasebeta

← Group #511936

Character table — Group #511936

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122444444444444888888888888888888888888816161616323232323232
order12442422244488888822244444444488888888888882244888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1
χ41111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-11-1-11-1-1-111-1-111-1-111-1-1-111-1-11-11-11-111-1-1
χ61111111111111111-1-1-11-1-11-1-1-111-1-111-1-111-1-1-111-1-1-11-11-11-1-111
χ71111111111111111-1-1-1-11-1-11-1-1-1-111-1-11111-1-1-1-1-1111-11-11-1-1-111
χ81111111111111111-1-1-1-11-1-11-1-1-1-111-1-11111-1-1-1-1-111-11-11-1111-1-1
χ9111111111111-1-1-1-111-11-1-11-1-1-111-1-1-1-111-1-1111-1-1111111-1-11-11-1
χ10111111111111-1-1-1-111-11-1-11-1-1-111-1-1-1-111-1-1111-1-111-1-1-1-111-11-11
χ11111111111111-1-1-1-111-1-11-1-11-1-1-1-11111-1-1-1-111111-1-11111-1-1-11-11
χ12111111111111-1-1-1-111-1-11-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1111-11-1
χ13111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11
χ14111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1
χ15111111111111-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-111111-11-1-11-111-1
χ16111111111111-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-11111-11-111-11-1-11
χ172222222-2-22-2-20000220020020000-2-2-2-200002-2-222000000000000
χ182222222-2-22-2-200002200-200-20000222200002-2-2-2-2000000000000
χ192222222-2-22-2-20000-2-20020020000-2-2220000-222-2-2000000000000
χ202222222-2-22-2-20000-2-200-200-2000022-2-20000-22222000000000000
χ21222222-22-2-22-200002202002000-2-20000-2-200-22-200220000000000
χ22222222-22-2-22-20000220-200-20002200002200-22-200-2-20000000000
χ23222222-22-2-22-20000-2-202002000-2-2000022002-2200-2-20000000000
χ24222222-22-2-22-20000-2-20-200-2000220000-2-2002-2200220000000000
χ25222222-2-22-2-22222222-200-2002200000000-2-2-2-2200000000000000
χ26222222-2-22-2-222222-2-2200200-2-200000000-2-222-200000000000000
χ27222222-2-22-2-22-2-2-2-222200200-2-20000000022-2-2200000000000000
χ28222222-2-22-2-22-2-2-2-2-2-2-200-20022000000002222-200000000000000
χ2922-2-22-222-2-2-22000000200-2002-200002i−2i2i−2i000002i−2i2i−2i0000000000
χ3022-2-22-222-2-2-22000000200-2002-20000−2i2i−2i2i00000−2i2i−2i2i0000000000
χ3122-2-22-222-2-2-22000000-200200-2200002i−2i−2i2i000002i−2i−2i2i0000000000
χ3222-2-22-222-2-2-22000000-200200-220000−2i2i2i−2i00000−2i2i2i−2i0000000000
χ3322-2-22-22-22-22-22i2i−2i−2i000200-20002-2002i−2i002i−2i000−2i2i000000000000
χ3422-2-22-22-22-22-22i2i−2i−2i000-2002000-2200−2i2i002i−2i0002i−2i000000000000
χ3522-2-22-22-22-22-2−2i−2i2i2i000200-20002-200−2i2i00−2i2i0002i−2i000000000000
χ3622-2-22-22-22-22-2−2i−2i2i2i000-2002000-22002i−2i00−2i2i000−2i2i000000000000
χ3722-2-22-2-2222-2-22i2i−2i−2i0000200-200002-200−2i2i−2i2i000002i−2i0000000000
χ3822-2-22-2-2222-2-22i2i−2i−2i0000-20020000-22002i−2i−2i2i00000−2i2i0000000000
χ3922-2-22-2-2222-2-2−2i−2i2i2i0000200-200002-2002i−2i2i−2i00000−2i2i0000000000
χ4022-2-22-2-2222-2-2−2i−2i2i2i0000-20020000-2200−2i2i2i−2i000002i−2i0000000000
χ4122-2-22-2-2-2-2222000000222-2-2-2-22-22-2200000000000000000000000
χ4222-2-22-2-2-2-22220000002-2-2-222-222-22-200000000000000000000000
χ4322-2-22-2-2-2-2222000000-22-22-222-2-222-200000000000000000000000
χ4422-2-22-2-2-2-2222000000-2-2222-22-22-2-2200000000000000000000000
χ4544-4-4-4400000000004-4000000000000000000000000022-2-2000000
χ4644-4-4-4400000000004-40000000000000000000000000-2-222000000
χ4744-4-4-440000000000-4400000000000000000000000002-2-22000000
χ4844-4-4-440000000000-440000000000000000000000000-222-2000000
χ498888-8-800000000000000000000000000000000000000000000000
χ508-88i−8i000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000
χ518-88i−8i00000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000
χ528-8−8i8i000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000
χ538-8−8i8i00000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000

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