Finite Group Databasebeta

← Group #314608

Character table — Group #314608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444224444444444224444444444444488888888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ17222222222222222222222222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000
χ212222-2-2-2-22200000000-2-222-2-222-2-22-200000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222-2-2-2-22200000000-2-222-2-222-2-22-20000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ232222-2-2-2-22200000000-2-222-2-2-2-222-220000002i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ242222-2-2-2-22200000000-2-222-2-2-2-222-22000000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ252222-2-2-2-22200000000-2-2-2-22222-2-2-2200000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ262222-2-2-2-22200000000-2-2-2-22222-2-2-220000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ272222-2-2-2-22200000000-2-2-2-222-2-2222-20000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ282222-2-2-2-22200000000-2-2-2-222-2-2222-2000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ292222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i2200002-22-2002i−2i00000000000000000000002-2002i−2i00000000
χ302222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i2200002-22-2002i−2i0000000000000000000000-2200−2i2i00000000
χ312222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i220000-22-2200−2i2i000000000000000000002-2002i−2i0000000000
χ322222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i220000-22-2200−2i2i00000000000000000000-2200−2i2i0000000000
χ332222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i2200002-22-200−2i2i00000000000000000000002-200−2i2i00000000
χ342222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i2200002-22-200−2i2i0000000000000000000000-22002i−2i00000000
χ352222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i220000-22-22002i−2i000000000000000000002-200−2i2i0000000000
χ362222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i220000-22-22002i−2i00000000000000000000-22002i−2i0000000000
χ3722-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i2-22-22-2000000002i−2i000000000000000000000000002−2i2−i22−2i2−i2
χ3822-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i2-22-22-2000000002i−2i00000000000000000000000000−22−i2i2−22−i2i2
χ3922-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i2-2-22-2200000000−2i2i000000000000000000000000002−2i2−i2−22−i2i2
χ4022-2-2-2-2222-22i2i−2i−2i2i2i−2i−2i2-2-22-2200000000−2i2i00000000000000000000000000−22−i2i22−2i2−i2
χ4122-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i2-22-22-200000000−2i2i000000000000000000000000002−2−i2i22−2−i2i2
χ4222-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i2-22-22-200000000−2i2i00000000000000000000000000−22i2−i2−22i2−i2
χ4322-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i2-2-22-22000000002i−2i000000000000000000000000002−2−i2i2−22i2−i2
χ4422-2-2-2-2222-2−2i−2i2i2i−2i−2i2i2i2-2-22-22000000002i−2i00000000000000000000000000−22i2−i22−2−i2i2
χ4544444444-4-400000000-4-400004-4-440000000000000000000000000000000000000000
χ4644444444-4-400000000-4-40000-444-40000000000000000000000000000000000000000
χ4744-4-444-4-44-400000000-444-4-4400000000000000000000000000000000000000000000
χ4844-4-444-4-44-400000000-44-444-400000000000000000000000000000000000000000000
χ4944-4-444-4-4-4444-4-4-4-4444-4000000000000000000000000000000000000000000000000
χ5044-4-444-4-4-44-4-44444-4-44-4000000000000000000000000000000000000000000000000
χ5144-4-4-4-444-4400000000-44000000000000004i−4i00000000000000000000000000000000
χ5244-4-4-4-444-4400000000-4400000000000000−4i4i00000000000000000000000000000000
χ534-44-44i−4i4i−4i002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ30000000000000000
χ544-44-44i−4i4i−4i002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ30000000000000000
χ554-44-44i−4i4i−4i00−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ30000000000000000
χ564-44-44i−4i4i−4i00−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000000−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ30000000000000000
χ574-44-4−4i4i−4i4i002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
χ584-44-4−4i4i−4i4i002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ594-44-4−4i4i−4i4i00−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ604-44-4−4i4i−4i4i00−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
χ614-4-444i−4i−4i4i002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000002ζ−2ζ2ζ3−2ζ300002ζ3−2ζ32ζ−2ζ00000000000000000000
χ624-4-444i−4i−4i4i002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000000−2ζ2ζ−2ζ32ζ30000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ634-4-444i−4i−4i4i00−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000002ζ−2ζ2ζ3−2ζ30000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ644-4-444i−4i−4i4i00−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000−2ζ2ζ−2ζ32ζ300002ζ3−2ζ32ζ−2ζ00000000000000000000
χ654-4-44−4i4i4i−4i002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000002ζ3−2ζ32ζ−2ζ00002ζ−2ζ2ζ3−2ζ300000000000000000000
χ664-4-44−4i4i4i−4i002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000−2ζ32ζ3−2ζ2ζ0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ674-4-44−4i4i4i−4i00−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000002ζ3−2ζ32ζ−2ζ0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ684-4-44−4i4i4i−4i00−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000000−2ζ32ζ3−2ζ2ζ00002ζ−2ζ2ζ3−2ζ300000000000000000000

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