Finite Group Databasebeta

← Group #498264

Character table — Group #498264

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12224444224444448888888844888888888888161616161616161616161616161616162244444488881616161616161616444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1
χ171111-1-1-1-1-1-111-1-11111-1-1-1-1111-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−iii−i−i11-1-111-1-11-11-11-1i−ii−ii−i
χ181111-1-1-1-1-1-111-1-11111-1-1-1-1111-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111i−ii−i−i−iii11-1-111-1-1-11-11-11−ii−ii−ii
χ191111-1-1-1-1-1-111-1-11111-1-1-1-1111-1ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−i−i−iii-1-111-1-1111-1-11-11i−ii−i−ii
χ201111-1-1-1-1-1-111-1-11111-1-1-1-1111-1ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−iii−i−i-1-111-1-111-111-11-1−ii−iii−i
χ211111-1-1-1-1-1-111-1-11111-1-1-1-1111-1−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−iiii−i−i-1-111-1-1111-1-11-11−ii−iii−i
χ221111-1-1-1-1-1-111-1-11111-1-1-1-1111-1−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−ii−ii−i−iii-1-111-1-111-111-11-1i−ii−i−ii
χ231111-1-1-1-1-1-111-1-11111-1-1-1-1111-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii−i−iii11-1-111-1-11-11-11-1−ii−ii−ii
χ241111-1-1-1-1-1-111-1-11111-1-1-1-1111-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111−ii−iiii−i−i11-1-111-1-1-11-11-11i−ii−ii−i
χ251111-1-1-1-1-1-1-1-1111111-1-1-1-111-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1i−i−iiii−i−i11-1-1-1-111-111-1-11i−i−ii−ii
χ261111-1-1-1-1-1-1-1-1111111-1-1-1-111-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111i−i−ii−i−iii11-1-1-1-1111-1-111-1−iii−ii−i
χ271111-1-1-1-1-1-1-1-1111111-1-1-1-111-11ii−i−i−i−iii-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1i−i−ii−i−iii-1-11111-1-1-11-111-1i−i−iii−i
χ281111-1-1-1-1-1-1-1-1111111-1-1-1-111-11ii−i−i−i−iii-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−iiii−i−i-1-11111-1-11-11-1-11−iii−i−ii
χ291111-1-1-1-1-1-1-1-1111111-1-1-1-111-11−i−iiiii−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1−iii−iii−i−i-1-11111-1-1-11-111-1−iii−i−ii
χ301111-1-1-1-1-1-1-1-1111111-1-1-1-111-11−i−iiiii−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−iii−i−i−iii-1-11111-1-11-11-1-11i−i−iii−i
χ311111-1-1-1-1-1-1-1-1111111-1-1-1-111-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−iii−i−i−iii11-1-1-1-111-111-1-11−iii−ii−i
χ321111-1-1-1-1-1-1-1-1111111-1-1-1-111-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111−iii−iii−i−i11-1-1-1-1111-1-111-1i−i−ii−ii
χ332222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000-2-2-2-2000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000002222000000000000000000000000
χ352222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000-2-222000000000000000000000000
χ362222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000022-2-2000000000000000000000000
χ3722222222-2-22222-2-200000000-2-22-22-22-22-2000022−2−222−2−222−2−222−2−20000000000002−22−22−22−2000000000000
χ3822222222-2-22222-2-200000000-2-22-22-22-22-20000−2−222−2−222−2−222−2−222000000000000−22−22−22−22000000000000
χ3922222222-2-22222-2-200000000-2-2-22-22-22-22000022−2−222−2−222−2−222−2−2000000000000−22−22−22−22000000000000
χ4022222222-2-22222-2-200000000-2-2-22-22-22-220000−2−222−2−222−2−222−2−2220000000000002−22−22−22−2000000000000
χ4122222222-2-2-2-2-2-2-2-200000000222-22-2-22-22000022−2−222−2−2−2−222−2−2220000000000002−22−2−22−22000000000000
χ4222222222-2-2-2-2-2-2-2-200000000222-22-2-22-220000−2−222−2−22222−2−222−2−2000000000000−22−222−22−2000000000000
χ4322222222-2-2-2-2-2-2-2-20000000022-22-222-22-2000022−2−222−2−2−2−222−2−222000000000000−22−222−22−2000000000000
χ4422222222-2-2-2-2-2-2-2-20000000022-22-222-22-20000−2−222−2−22222−2−222−2−20000000000002−22−2−22−22000000000000
χ452222-2-2-2-22222-2-2-2-200000000-222i−2i−2i2i2i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ462222-2-2-2-22222-2-2-2-200000000-222i−2i−2i2i2i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ472222-2-2-2-22222-2-2-2-200000000-22−2i2i2i−2i−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ482222-2-2-2-22222-2-2-2-200000000-22−2i2i2i−2i−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ492222-2-2-2-222-2-222-2-2000000002-22i−2i−2i2i−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ502222-2-2-2-222-2-222-2-2000000002-22i−2i−2i2i−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ512222-2-2-2-222-2-222-2-2000000002-2−2i2i2i−2i2i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ522222-2-2-2-222-2-222-2-2000000002-2−2i2i2i−2i2i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ532222-2-2-2-2-2-222-2-222-2-22222-2-22-22i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000−2i2i−2i2i000000000000000000000000
χ542222-2-2-2-2-2-222-2-222-2-22222-2-22-2−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000002i−2i2i−2i000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-22222-2-2-222i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000−2i2i2i−2i000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-22222-2-2-22−2i−2i2i2i2i2i−2i−2i22-2-2000000000000000000002i−2i−2i2i000000000000000000000000
χ5722-2-222-2-22-200002-22222-2-2-2-2000000000000002-22-22-22-2000000002-22-200002-22-200000000000000000000
χ5822-2-222-2-22-200002-22222-2-2-2-2000000000000002-22-22-22-200000000-22-220000-22-2200000000000000000000
χ5922-2-222-2-22-200002-22222-2-2-2-200000000000000-22-22-22-22000000002-22-20000-22-2200000000000000000000
χ6022-2-222-2-22-200002-22222-2-2-2-200000000000000-22-22-22-2200000000-22-2200002-22-200000000000000000000
χ6122-2-2-2-222-2200002-222-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i000000002-2-2200002i−2i−2i2i00000000000000000000
χ6222-2-2-2-222-2200002-222-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i00000000-222-20000−2i2i2i−2i00000000000000000000
χ6322-2-2-2-222-2200002-222-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i000000002-2-220000−2i2i2i−2i00000000000000000000
χ6422-2-2-2-222-2200002-222-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i00000000-222-200002i−2i−2i2i00000000000000000000
χ6544-4-444-4-44-400004-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-440000-44000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ6744-4-444-4-4-440000-440000000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ6844-4-4-4-4444-40000-4400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ6944-4-4-4-4444-40000-440000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ7044-4-4-4-444-4400004-4-4-444-4-44400000000000000000000000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i0000000022−222i2−2i22i2−2i222−2200000000000000000000002ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ300000000000000000000000000000000
χ724-44-44i−4i4i−4i0000000022−222i2−2i22i2−2i222−220000000000000000000000−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ300000000000000000000000000000000
χ734-44-44i−4i4i−4i00000000−2222−2i22i2−2i22i2−222200000000000000000000002ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000
χ744-44-44i−4i4i−4i00000000−2222−2i22i2−2i22i2−22220000000000000000000000−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000
χ754-44-4−4i4i−4i4i0000000022−22−2i22i2−2i22i222−2200000000000000000000002ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000
χ764-44-4−4i4i−4i4i0000000022−22−2i22i2−2i22i222−220000000000000000000000−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000
χ774-44-4−4i4i−4i4i00000000−22222i2−2i22i2−2i2−222200000000000000000000002ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ300000000000000000000000000000000
χ784-44-4−4i4i−4i4i00000000−22222i2−2i22i2−2i2−22220000000000000000000000−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ300000000000000000000000000000000
χ794-4-444i−4i−4i4i004i−4i4-40022−222i2−2i2−2i22i2−222200000000002i2−2i222−22000000000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i004i−4i4-400−2222−2i22i22i2−2i222−220000000000−2i22i2−2222000000000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i00−4i4i-440022−222i2−2i2−2i22i2−22220000000000−2i22i2−2222000000000000000000000000000000000000000000000000
χ824-4-444i−4i−4i4i00−4i4i-4400−2222−2i22i22i2−2i222−2200000000002i2−2i222−22000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i004i−4i-440022−22−2i22i22i2−2i2−222200000000002i2−2i2−2222000000000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i004i−4i-4400−22222i2−2i2−2i22i222−220000000000−2i22i222−22000000000000000000000000000000000000000000000000
χ854-4-44−4i4i4i−4i00−4i4i4-40022−22−2i22i22i2−2i2−22220000000000−2i22i222−22000000000000000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i00−4i4i4-400−22222i2−2i2−2i22i222−2200000000002i2−2i2−2222000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.