Finite Group Databasebeta

← Group #507793

Character table — Group #507793

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order1244222444888888888888888824444422444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-11-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ611111111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-1-1-1111111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-1111-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1111-1-11111-1-1-1-1-1-111-1-111
χ121111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-111-1-1-1-111-1-111-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-11111-1-111-1-1-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ2122-2-2222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-2000000000000000000002−2i2−i2i2−i22−2
χ2222-2-2222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-200000000000000000000−22−i2i2−i2i2−22
χ2322-2-2222-2-2-22i2i−2i−2i−2i−2i2i2i00000000-22000000000000000000002−2i2−i2−i2i2−22
χ2422-2-2222-2-2-22i2i−2i−2i−2i−2i2i2i00000000-2200000000000000000000−22−i2i2i2−i22−2
χ2522-2-2222-2-2-2−2i−2i2i2i2i2i−2i−2i00000000-22000000000000000000002−2−i2i2i2−i2−22
χ2622-2-2222-2-2-2−2i−2i2i2i2i2i−2i−2i00000000-2200000000000000000000−22i2−i2−i2i22−2
χ2722-2-2222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-2000000000000000000002−2−i2i2−i2i22−2
χ2822-2-2222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-200000000000000000000−22i2−i2i2−i2−22
χ2922-2-22-2-222-200002i−2i2i−2i000022-2-200002i−2i00002-2002i−2i00000000000000
χ3022-2-22-2-222-200002i−2i2i−2i000022-2-200002i−2i0000-2200−2i2i00000000000000
χ3122-2-22-2-222-200002i−2i2i−2i0000-2-2220000−2i2i20-20000000002i−2i0000000000
χ3222-2-22-2-222-200002i−2i2i−2i0000-2-2220000−2i2i-202000000000−2i2i0000000000
χ3322-2-22-2-222-20000−2i2i−2i2i000022-2-20000−2i2i00002-200−2i2i00000000000000
χ3422-2-22-2-222-20000−2i2i−2i2i000022-2-20000−2i2i0000-22002i−2i00000000000000
χ3522-2-22-2-222-20000−2i2i−2i2i0000-2-22200002i−2i20-2000000000−2i2i0000000000
χ3622-2-22-2-222-20000−2i2i−2i2i0000-2-22200002i−2i-2020000000002i−2i0000000000
χ3722-2-2-22-22-222i−2i2i−2i000000002-22-2002i−2i000000002-2002i−2i000000000000
χ3822-2-2-22-22-222i−2i2i−2i000000002-22-2002i−2i00000000-2200−2i2i000000000000
χ3922-2-2-22-22-222i−2i2i−2i00000000-22-2200−2i2i00020-200000000002i−2i00000000
χ4022-2-2-22-22-222i−2i2i−2i00000000-22-2200−2i2i000-2020000000000−2i2i00000000
χ4122-2-2-22-22-22−2i2i−2i2i000000002-22-200−2i2i000000002-200−2i2i000000000000
χ4222-2-2-22-22-22−2i2i−2i2i000000002-22-200−2i2i00000000-22002i−2i000000000000
χ4322-2-2-22-22-22−2i2i−2i2i00000000-22-22002i−2i00020-20000000000−2i2i00000000
χ4422-2-2-22-22-22−2i2i−2i2i00000000-22-22002i−2i000-20200000000002i−2i00000000
χ4544444-4-4-4-4400004-4-4400000000000000000000000000000000000000
χ4644444-4-4-4-440000-444-400000000000000000000000000000000000000
χ474444-44-4-44-44-4-44000000000000000000000000000000000000000000
χ484444-44-4-44-4-444-4000000000000000000000000000000000000000000
χ494444-4-444-4-40000000000004-4-44000000000000000000000000000000
χ504444-4-444-4-4000000000000-444-4000000000000000000000000000000
χ5144-4-4-4-44-444000000004i4i−4i−4i0000000000000000000000000000000000
χ5244-4-4-4-44-44400000000−4i−4i4i4i0000000000000000000000000000000000
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.