Finite Group Databasebeta

← Group #420376

Character table — Group #420376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12442222222444444488882222444444444444888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111
χ51111111111111111111111-1-111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ11111111111111111111-1-1-1-111-1-111-1-111111111-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ13111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-1-1-111-1-1
χ1722222-2-22-22-2222-2-2-2-20000002-2002-22i2i−2i−2i0000000000000000000000002i−2i00
χ1822222-2-22-22-2222-2-2-2-20000002-2002-2−2i−2i2i2i000000000000000000000000−2i2i00
χ1922222-2-22-22-2222-2-2-2-2000000-2200-222i2i−2i−2i000000000000000000000000−2i2i00
χ2022222-2-22-22-2222-2-2-2-2000000-2200-22−2i−2i2i2i0000000000000000000000002i−2i00
χ2122222-2-2-22-222-2-2-22-22000000000000000022-2-20022-2-200002-2000000000000
χ2222222-2-2-22-222-2-2-22-22000000000000000022-2-200-2-2220000-22000000000000
χ2322222-2-2-22-222-2-2-22-220000000000000000-2-2220022-2-20000-22000000000000
χ2422222-2-2-22-222-2-2-22-220000000000000000-2-22200-2-22200002-2000000000000
χ252222-22-2-222-2-22-2-2-22222222-2002-20000000000-2-200000000002-20000000000
χ262222-22-2-222-2-22-2-2-2222222-2200-220000000000-2-20000000000-220000000000
χ272222-22-2-222-2-22-2-2-222-2-2-2-22-2002-20000000000220000000000-220000000000
χ282222-22-2-222-2-22-2-2-222-2-2-2-2-2200-2200000000002200000000002-20000000000
χ2922-2-2222-2-2-2-2-222-22-220000000000002i−2i2i−2i0000002-22-200000000002i−2i000000
χ3022-2-2222-2-2-2-2-222-22-220000000000002i−2i2i−2i000000-22-220000000000−2i2i000000
χ3122-2-2222-2-2-2-2-222-22-22000000000000−2i2i−2i2i0000002-22-20000000000−2i2i000000
χ3222-2-2222-2-2-2-2-222-22-22000000000000−2i2i−2i2i000000-22-2200000000002i−2i000000
χ3322-2-22-2-22-22-2-2-2-2222200002-200-220000000000002-2-222-20000000000000000
χ3422-2-22-2-22-22-2-2-2-2222200002-200-22000000000000-222-2-220000000000000000
χ3522-2-22-2-22-22-2-2-2-222220000-22002-20000000000002-2-22-220000000000000000
χ3622-2-22-2-22-22-2-2-2-222220000-22002-2000000000000-222-22-20000000000000000
χ3722-2-22-2-2-22-22-2222-22-22i2i−2i−2i000000002-2-2200002i−2i0000002i−2i00000000000000
χ3822-2-22-2-2-22-22-2222-22-22i2i−2i−2i00000000-222-200002i−2i000000−2i2i00000000000000
χ3922-2-22-2-2-22-22-2222-22-2−2i−2i2i2i000000002-2-220000−2i2i000000−2i2i00000000000000
χ4022-2-22-2-2-22-22-2222-22-2−2i−2i2i2i00000000-222-20000−2i2i0000002i−2i00000000000000
χ4122-2-2-22-2-222-22-2222-2-20000002200-2-200002i−2i2i−2i00000000000000000000002i−2i
χ4222-2-2-22-2-222-22-2222-2-20000002200-2-20000−2i2i−2i2i0000000000000000000000−2i2i
χ4322-2-2-22-2-222-22-2222-2-2000000-2-2002200002i−2i2i−2i0000000000000000000000−2i2i
χ4422-2-2-22-2-222-22-2222-2-2000000-2-200220000−2i2i−2i2i00000000000000000000002i−2i
χ4522-2-2-2-2222-2-222-2-222-22i2i−2i−2i0000000000002i−2i−2i2i−2i2i00000000000000002-20000
χ4622-2-2-2-2222-2-222-2-222-22i2i−2i−2i000000000000−2i2i2i−2i−2i2i0000000000000000-220000
χ4722-2-2-2-2222-2-222-2-222-2−2i−2i2i2i0000000000002i−2i−2i2i2i−2i0000000000000000-220000
χ4822-2-2-2-2222-2-222-2-222-2−2i−2i2i2i000000000000−2i2i2i−2i2i−2i00000000000000002-20000
χ4922-2-2-2-22-2-2222-22-2-2220000222-2-2-2-2200000000000000000000002-200000000
χ5022-2-2-2-22-2-2222-22-2-222000022-22-2-22-20000000000000000000000-2200000000
χ5122-2-2-2-22-2-2222-22-2-2220000-2-22-222-220000000000000000000000-2200000000
χ5222-2-2-2-22-2-2222-22-2-2220000-2-2-22222-200000000000000000000002-200000000
χ534444444-4-4-4-44-4-44-44-400000000000000000000000000000000000000000000
χ544444-44-44-4-44-4-44-444-400000000000000000000000000000000000000000000
χ554444-4-4444-4-4-4-444-4-4400000000000000000000000000000000000000000000
χ564444-4-44-4-444-44-444-4-400000000000000000000000000000000000000000000
χ5744-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ5844-4-4-44-44-4-4444-44-4-4400000000000000000000000000000000000000000000
χ598-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000
χ608-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000
χ618-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000
χ628-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000

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