Finite Group Databasebeta

← Group #119813

Character table — Group #119813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888888888888888888882244444444448888
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
χ91111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11-11−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-111111-11-1ii−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-11−i−iiiii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-111111-11-1−i−iiiii−i−i-1-111
χ141111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-11-11ii−i−i−i−iii11-1-1
χ151111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii−i−iii11-1-1
χ161111-1-1-1-111-1-1-1-111-1-1-1-1111-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−iii−i−i-1-111
χ1722222222222222-2-2-2-2-2-222222-2-22-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222222-2-22-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-2222222-2-2-22222-2-2-2-2-20000000000000000000000000000000000002i−2i2i−2i00000000
χ202222222222-2-2-2-2222222-2-2-22222-2-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i00000000
χ212222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-22-22-22222-2-222-2-2-2-2-2-22-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-22-22-22222-2-222-2-2-2-2-2-22-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-22-22-2-2-2-2-22222-2-2-222-2-22-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-22-22-2-2-2-2-22222-2-2-222-2-22-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-22-222222-2-2-2-22-2-2-2-22-22-2200000000000000000000000000000000000000002-22-20000
χ2822222222-2-2-22-222222-2-2-2-22-2-2-2-22-22-220000000000000000000000000000000000000000-22-220000
χ2922222222-2-2-22-22-2-2-2-222-2-22-2-22222-22-2000000000000000000000000000000002-2-22000000000000
χ3022222222-2-2-22-22-2-2-2-222-2-22-2-22222-22-200000000000000000000000000000000-222-2000000000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2-222-2-2-2220000000000000000000000000000000000002-2-2200000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2-222-2-2-222000000000000000000000000000000000000-222-200000000
χ332222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-2-2-2-22222222-2-2-2-22-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-22222222-2-2-2-22-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-2-2-2-22-22-222-2-222-2-2222-2-22-222-200000000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-22-22-222-2-222-2-2222-2-22-222-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-22-22-2-2-222-2-2-2-22222222-2-220000000000000000000000000000000022-2-2000000000000
χ402222-2-2-2-2-2-22-22-2-2-222-2-2-2-22222222-2-2200000000000000000000000000000000-2-222000000000000
χ412222-2-2-2-2-2-2-22-2222-2-22222-222-2-2-22-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ422222-2-2-2-2-2-2-22-2222-2-22222-222-2-2-22-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ432222-2-2-2-2-2-2-22-22-2-222-2-222-22222-2-222-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ442222-2-2-2-2-2-2-22-22-2-222-2-222-22222-2-222-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ452-2-2222-2-22-222-2-20000002-2-22-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ462-2-2222-2-22-222-2-20000002-2-22-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ472-2-2222-2-22-222-2-20000002-2-22-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ482-2-2222-2-22-222-2-20000002-2-22-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ492-2-2222-2-2-222-2-220000002-22-2200-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ502-2-2222-2-2-222-2-220000002-22-2200-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ512-2-2222-2-2-222-2-220000002-22-2200-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ522-2-2222-2-2-222-2-220000002-22-2200-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ532-2-22-2-2222-2-2-2220000002-2-2-22002000022−2−222−2−2−2−222−2−222002-200-222−22−2−22−220000000000000000
χ542-2-22-2-2222-2-2-2220000002-2-2-22002000022−2−222−2−2−2−222−2−22200-22002-2−22−222−22−20000000000000000
χ552-2-22-2-2222-2-2-2220000002-2-2-220020000−2−222−2−22222−2−222−2−2002-200-22−22−222−22−20000000000000000
χ562-2-22-2-2222-2-2-2220000002-2-2-220020000−2−222−2−22222−2−222−2−200-22002-22−22−2−22−220000000000000000
χ572-2-22-2-222-22-222-20000002-222-200-2000022−2−2−2−222−2−22222−2−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ582-2-22-2-222-22-222-20000002-222-200-2000022−2−2−2−222−2−22222−2−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ592-2-22-2-222-22-222-20000002-222-200-20000−2−22222−2−222−2−2−2−2222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ602-2-22-2-222-22-222-20000002-222-200-20000−2−22222−2−222−2−2−2−222−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ6144-4-44i−4i4i−4i00000000004i−4i000004-40000000002+2i−2−2i2+2i−2−2i00002−2i−2+2i2−2i−2+2i00000000000000000000000000000000
χ6244-4-44i−4i4i−4i00000000004i−4i000004-4000000000−2−2i2+2i−2−2i2+2i0000−2+2i2−2i−2+2i2−2i00000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000000000−4i4i00000-44000002−2i−2+2i2−2i−2+2i00002+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
χ6444-4-44i−4i4i−4i0000000000−4i4i00000-4400000−2+2i2−2i−2+2i2−2i0000−2−2i2+2i−2−2i2+2i000000000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00000000004i−4i00000-44000002+2i−2−2i2+2i−2−2i00002−2i−2+2i2−2i−2+2i000000000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00000000004i−4i00000-4400000−2−2i2+2i−2−2i2+2i0000−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ6744-4-4−4i4i−4i4i0000000000−4i4i000004-40000000002−2i−2+2i2−2i−2+2i00002+2i−2−2i2+2i−2−2i00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i0000000000−4i4i000004-4000000000−2+2i2−2i−2+2i2−2i0000−2−2i2+2i−2−2i2+2i00000000000000000000000000000000
χ694-44-44i−4i−4i4i0000004i−4i4-4000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ704-44-44i−4i−4i4i0000004i−4i4-400000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ714-44-44i−4i−4i4i000000−4i4i-44000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ724-44-44i−4i−4i4i000000−4i4i-4400000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ734-44-4−4i4i4i−4i0000004i−4i-44000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ744-44-4−4i4i4i−4i0000004i−4i-4400000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ754-44-4−4i4i4i−4i000000−4i4i4-4000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ764-44-4−4i4i4i−4i000000−4i4i4-400000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ774-4-4444-4-44-4-4-444000000-4444-400-40000000000000000000000000000000000000000000000000000
χ784-4-4444-4-4-44-444-4000000-44-4-440040000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-444-4-4000000-444-4400-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-444-4-44000000-44-44-40040000000000000000000000000000000000000000000000000000

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