Finite Group Databasebeta

← Group #119221

Character table — Group #119221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888844444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111-1-1-11-111-1-1-11111-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222222-2-2-2-2-2-2-2-22-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ182222222222222222222-2-2-2-2-2-2-2-22-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222-2-2-22-222-2-2-2-2-2-2-22222-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ20222222222-2-2-22-222-2-2-2-2-2-2-22222-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2122222222-22-2-2-22-2-22-2-22222-2-2-2-22-222-20000000000000000000000000000000000002i−2i2i−2i00000000
χ2222222222-22-2-2-22-2-22-2-22222-2-2-2-22-222-2000000000000000000000000000000000000−2i2i−2i2i00000000
χ2322222222-22-2-2-22-2-22-2-2-2-2-2-2222222-2-22000000000000000000000000000000000000000000002-22-2
χ2422222222-22-2-2-22-2-22-2-2-2-2-2-2222222-2-2200000000000000000000000000000000000000000000-22-22
χ2522222222-2-222-2-2-2-2-22222222222-2-2-2-2-20000000000000000000000000000000000002i−2i−2i2i00000000
χ2622222222-2-222-2-2-2-2-22222222222-2-2-2-2-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ2722222222-2-222-2-2-2-2-222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-222-2-2-2-2-222-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i2i−2i
χ292222-2-2-2-2222222-2-2-2-2-222-2-222-2-2-2-22-22000000000000000000000000000000002-22-2000000000000
χ302222-2-2-2-2222222-2-2-2-2-222-2-222-2-2-2-22-2200000000000000000000000000000000-22-22000000000000
χ312222-2-2-2-2222222-2-2-2-2-2-2-222-2-222-22-22-200000000000000000000000000000000000000002-22-20000
χ322222-2-2-2-2222222-2-2-2-2-2-2-222-2-222-22-22-20000000000000000000000000000000000000000-22-220000
χ332222-2-2-2-22-2-2-22-2-2-222222-2-2-2-2222-2-222000000000000000000000000000000002-2-22000000000000
χ342222-2-2-2-22-2-2-22-2-2-222222-2-2-2-2222-2-22200000000000000000000000000000000-222-2000000000000
χ352222-2-2-2-22-2-2-22-2-2-2222-2-22222-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-22-2-2-22-2-2-2222-2-22222-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-22-2-2-2222-22222-2-2-2-222-222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ382222-2-2-2-2-22-2-2-2222-22222-2-2-2-222-222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ392222-2-2-2-2-22-2-2-2222-222-2-22222-2-2-2-2-2220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ402222-2-2-2-2-22-2-2-2222-222-2-22222-2-2-2-2-222000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ412222-2-2-2-2-2-222-2-2222-2-222-2-222-2-222-22-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ422222-2-2-2-2-2-222-2-2222-2-222-2-222-2-222-22-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ432222-2-2-2-2-2-222-2-2222-2-2-2-222-2-2222-22-2200000000000000000000000022-2-2-2-2220000000000000000
χ442222-2-2-2-2-2-222-2-2222-2-2-2-222-2-2222-22-22000000000000000000000000-2-22222-2-20000000000000000
χ4522-2-222-2-2222-2-2-22-222-200000000-2000022−2−222−2−222−2−222−2−2002-2002-22−22−22−22−20000000000000000
χ4622-2-222-2-2222-2-2-22-222-200000000-2000022−2−222−2−222−2−222−2−200-2200-22−22−22−22−220000000000000000
χ4722-2-222-2-2222-2-2-22-222-200000000-20000−2−222−2−222−2−222−2−222002-2002-2−22−22−22−220000000000000000
χ4822-2-222-2-2222-2-2-22-222-200000000-20000−2−222−2−222−2−222−2−22200-2200-222−22−22−22−20000000000000000
χ4922-2-222-2-22-2-22-222-2-2-22000000002000022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ5022-2-222-2-22-2-22-222-2-2-22000000002000022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ5122-2-222-2-22-2-22-222-2-2-220000000020000−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ5222-2-222-2-22-2-22-222-2-2-220000000020000−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-2-2-2-222-22-222-22-2-22-20000000020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ5422-2-2-2-222-22-222-22-2-22-20000000020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ5522-2-2-2-222-22-222-22-2-22-20000000020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ5622-2-2-2-222-22-222-22-2-22-20000000020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ5722-2-2-2-222-2-22-2222-22-2200000000-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22i−2i00−2i2i00−222−22−2−220000000000000000
χ5822-2-2-2-222-2-22-2222-22-2200000000-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2i2i002i−2i002−2−22−222−20000000000000000
χ5922-2-2-2-222-2-22-2222-22-2200000000-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22i−2i00−2i2i002−2−22−222−20000000000000000
χ6022-2-2-2-222-2-22-2222-22-2200000000-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2i2i002i−2i00−222−22−2−220000000000000000
χ6144-4-444-4-4-44-444-4-444-4400000000-40000000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-4-44-444-44-44-40000000040000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444444-4-4-4-44-4-440000000040000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-44-44-4444-400000000-40000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000000004i−4i4-4000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000000004i−4i4-400000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000000−4i4i-44000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000000−4i4i-4400000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000000004i−4i-44000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000000004i−4i-4400000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000000−4i4i4-4000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000000−4i4i4-400000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ734-4-444i−4i−4i4i000000000004-44i−4i000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000
χ744-4-444i−4i−4i4i000000000004-44i−4i00000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000
χ754-4-444i−4i−4i4i00000000000-44−4i4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ764-4-444i−4i−4i4i00000000000-44−4i4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i000000000004-4−4i4i000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000
χ784-4-44−4i4i4i−4i000000000004-4−4i4i00000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000
χ794-4-44−4i4i4i−4i00000000000-444i−4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ804-4-44−4i4i4i−4i00000000000-444i−4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000

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