Finite Group Databasebeta

← Group #474761

Character table — Group #474761

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222222244448888888888161616161616161616161616161616161616161616161616
order12442222222444444488884444888888244444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111
χ17222222-2-22-2-2-222-2-22-20000000022-2-2000000000000002i−2i2i−2i00000000
χ18222222-2-22-2-2-222-2-22-20000000022-2-200000000000000−2i2i−2i2i00000000
χ19222222-2-22-2-2-222-2-22-200000000-2-222000000000000002i−2i−2i2i00000000
χ20222222-2-22-2-2-222-2-22-200000000-2-22200000000000000−2i2i2i−2i00000000
χ212222-2-2222-2-2-2-2-2222-2000000002-22-20000000000002i−2i00002i−2i000000
χ222222-2-2222-2-2-2-2-2222-2000000002-22-2000000000000−2i2i0000−2i2i000000
χ232222-2-2222-2-2-2-2-2222-200000000-22-220000000000002i−2i0000−2i2i000000
χ242222-2-2222-2-2-2-2-2222-200000000-22-22000000000000−2i2i00002i−2i000000
χ252222-2-2-2-22222-2-2-2-222222222-2-22-2-22-2-2000000000000000000000000
χ262222-2-2-2-22222-2-2-2-2222222-2-222-222-2-2-2000000000000000000000000
χ272222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-222-222000000000000000000000000
χ282222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2222-2-2222000000000000000000000000
χ2922-2-222-2-22-2-22-2-222-2200002i−2i2i−2i0000002-200000000000000002i−2i0000
χ3022-2-222-2-22-2-22-2-222-2200002i−2i2i−2i000000-220000000000000000−2i2i0000
χ3122-2-222-2-22-2-22-2-222-220000−2i2i−2i2i0000002-20000000000000000−2i2i0000
χ3222-2-222-2-22-2-22-2-222-220000−2i2i−2i2i000000-2200000000000000002i−2i0000
χ3322-2-22-22-2-2-2222-22-22-22i2i−2i−2i000000002i−2i0000002-2000000000000002i−2i
χ3422-2-22-22-2-2-2222-22-22-22i2i−2i−2i000000002i−2i000000-2200000000000000−2i2i
χ3522-2-22-22-2-2-2222-22-22-2−2i−2i2i2i00000000−2i2i0000002-200000000000000−2i2i
χ3622-2-22-22-2-2-2222-22-22-2−2i−2i2i2i00000000−2i2i000000-22000000000000002i−2i
χ3722-2-2-22-22-2-222-22-222-22i2i−2i−2i00000000−2i2i00002-2000000000000002i−2i00
χ3822-2-2-22-22-2-222-22-222-22i2i−2i−2i00000000−2i2i0000-2200000000000000−2i2i00
χ3922-2-2-22-22-2-222-22-222-2−2i−2i2i2i000000002i−2i00002-200000000000000−2i2i00
χ4022-2-2-22-22-2-222-22-222-2−2i−2i2i2i000000002i−2i0000-22000000000000002i−2i00
χ4122-2-2-2-2222-2-2222-2-2-2200002i−2i−2i2i000000002-200002i−2i00000000000000
χ4222-2-2-2-2222-2-2222-2-2-2200002i−2i−2i2i00000000-220000−2i2i00000000000000
χ4322-2-2-2-2222-2-2222-2-2-220000−2i2i2i−2i000000002-20000−2i2i00000000000000
χ4422-2-2-2-2222-2-2222-2-2-220000−2i2i2i−2i00000000-2200002i−2i00000000000000
χ4544444-44-4-4-44-4-44-44-4400000000000000000000000000000000000000
χ4644444-4-44-44-44-444-4-4-400000000000000000000000000000000000000
χ474444-444-4-44-444-4-44-4-400000000000000000000000000000000000000
χ484444-44-44-4-44-44-44-4-4400000000000000000000000000000000000000
χ4944-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000
χ5044-4-44-4-44-44-4-44-4-444400000000000000000000000000000000000000
χ5144-4-4-444-4-44-4-4-444-44400000000000000000000000000000000000000
χ5244-4-4-4-4-4-4444-44444-4-400000000000000000000000000000000000000
χ538-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000
χ548-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000
χ558-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000
χ568-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000

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