Finite Group Databasebeta

← Group #229229

Character table — Group #229229

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12224444224444448888888844888888888888888888888888888844448888888888888888244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1
χ171111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1ii−i−iii−i−iii−i−i11-1-111-1-1iiii−i−i−i−i11-1-1i−ii−iii−i−i11-1-111-1-11-11-1i−ii−ii−i1-1
χ181111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1ii−i−iii−i−iii−i−i11-1-111-1-1iiii−i−i−i−i-1-111i−ii−i−i−iii11-1-111-1-1-11-11−ii−ii−ii-11
χ191111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1ii−i−i−i−iiiii−i−i-1-111-1-111−i−i−i−iiiii11-1-1−iii−iii−i−i11-1-1-1-111-111-1−ii−iii−i-11
χ201111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1ii−i−i−i−iiiii−i−i-1-111-1-111−i−i−i−iiiii-1-111−iii−i−i−iii11-1-1-1-1111-1-11i−ii−i−ii1-1
χ211111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1−i−iiiii−i−iii−i−i-1-111-1-111−i−i−i−iiiii11-1-1i−i−iiii−i−i-1-11111-1-11-1-11−iii−i−ii-11
χ221111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1−i−iiiii−i−iii−i−i-1-111-1-111−i−i−i−iiiii-1-111i−i−ii−i−iii-1-11111-1-1-111-1i−i−iii−i1-1
χ231111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1−i−iii−i−iiiii−i−i11-1-111-1-1iiii−i−i−i−i11-1-1−ii−iiii−i−i-1-111-1-111-11-11i−i−ii−ii1-1
χ241111-1-1-1-1-1-11-1-1111iiii−i−i−i−i1-1−i−iii−i−iiiii−i−i11-1-111-1-1iiii−i−i−i−i-1-111−ii−ii−i−iii-1-111-1-1111-11-1−iii−ii−i-11
χ251111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1ii−i−iii−i−i−i−iii11-1-111-1-1−i−i−i−iiiii11-1-1i−ii−i−i−iii-1-111-1-111-11-11−iii−ii−i1-1
χ261111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1ii−i−iii−i−i−i−iii11-1-111-1-1−i−i−i−iiiii-1-111i−ii−iii−i−i-1-111-1-1111-11-1i−i−ii−ii-11
χ271111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1ii−i−i−i−iii−i−iii-1-111-1-111iiii−i−i−i−i11-1-1−iii−i−i−iii-1-11111-1-11-1-11i−i−iii−i-11
χ281111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1ii−i−i−i−iii−i−iii-1-111-1-111iiii−i−i−i−i-1-111−iii−iii−i−i-1-11111-1-1-111-1−iii−i−ii1-1
χ291111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1−i−iiiii−i−i−i−iii-1-111-1-111iiii−i−i−i−i11-1-1i−i−ii−i−iii11-1-1-1-111-111-1i−ii−i−ii-11
χ301111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1−i−iiiii−i−i−i−iii-1-111-1-111iiii−i−i−i−i-1-111i−i−iiii−i−i11-1-1-1-1111-1-11−ii−iii−i1-1
χ311111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii11-1-1−ii−ii−i−iii11-1-111-1-11-11-1−ii−ii−ii1-1
χ321111-1-1-1-1-1-11-1-1111−i−i−i−iiiii1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii-1-111−ii−iiii−i−i11-1-111-1-1-11-11i−ii−ii−i-11
χ3322222222222-2-2-2-2200000000-2-22222222200002222-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ3422222222222-2-2-2-2200000000-2-22222-2-2-2-20000-2-2-2-2222200000000000022-2-2000000000000000000000000
χ3522222222222-2-2-2-2200000000-2-2-2-2-2-222220000-2-2-2-22222000000000000-2-222000000000000000000000000
χ3622222222222-2-2-2-2200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000000002222000000000000000000000000
χ3722222222-2-2-22222-222222222-2-200000000-2-2-2-200000000000000002-22-200002-22-200000000000000000000
χ3822222222-2-2-22222-222222222-2-200000000-2-2-2-20000000000000000-22-220000-22-2200000000000000000000
χ3922222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000002-22-20000-22-2200000000000000000000
χ4022222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-22-2200002-22-200000000000000000000
χ412222-2-2-2-222-2-2-222-22i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i00000000000000002-2-2200002i−2i−2i2i00000000000000000000
χ422222-2-2-2-222-2-2-222-22i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i0000000000000000-222-20000−2i2i2i−2i00000000000000000000
χ432222-2-2-2-222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i00000000000000002-2-220000−2i2i2i−2i00000000000000000000
χ442222-2-2-2-222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i0000000000000000-222-200002i−2i−2i2i00000000000000000000
χ452222-2-2-2-2-2-2222-2-2200000000-222i2i−2i−2i2i2i−2i−2i000022-2-2-2-222000000000000−2i2i−2i2i000000000000000000000000
χ462222-2-2-2-2-2-2222-2-2200000000-222i2i−2i−2i−2i−2i2i2i0000-2-22222-2-20000000000002i−2i−2i2i000000000000000000000000
χ472222-2-2-2-2-2-2222-2-2200000000-22−2i−2i2i2i2i2i−2i−2i0000-2-22222-2-2000000000000−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-2-2-2222-2-2200000000-22−2i−2i2i2i−2i−2i2i2i000022-2-2-2-2220000000000002i−2i2i−2i000000000000000000000000
χ4922-2-222-2-2-22-20000222−2−222−2−2002-22-22i−2i2i−2i2−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i20000000000002−22−2i2−i2i2−i2000000000000
χ5022-2-222-2-2-22-20000222−2−222−2−2002-22-2−2i2i−2i2i2−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i20000000000002−22−2−i2i2−i2i2000000000000
χ5122-2-222-2-2-22-20000222−2−222−2−200-22-222i−2i2i−2i2−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000−22−22i2−i2i2−i2000000000000
χ5222-2-222-2-2-22-20000222−2−222−2−200-22-22−2i2i−2i2i2−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000−22−22−i2i2−i2i2000000000000
χ5322-2-222-2-2-22-200002−2−222−2−222002-22-22i−2i2i−2i−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000−22−22−i2i2−i2i2000000000000
χ5422-2-222-2-2-22-200002−2−222−2−222002-22-2−2i2i−2i2i−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000−22−22i2−i2i2−i2000000000000
χ5522-2-222-2-2-22-200002−2−222−2−22200-22-222i−2i2i−2i−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i20000000000002−22−2−i2i2−i2i2000000000000
χ5622-2-222-2-2-22-200002−2−222−2−22200-22-22−2i2i−2i2i−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i20000000000002−22−2i2−i2i2−i2000000000000
χ5722-2-2-2-2222-2-200002i2i2−i2−i2−i2−i2i2i2002i−2i−2i2i2-2-22i2−i2−i2i2−2i2i2i−2i000022−2−2−2−2220000000000002−2−22−i2i2i2−i2000000000000
χ5822-2-2-2-2222-2-200002i2i2−i2−i2−i2−i2i2i2002i−2i−2i2i-222-2i2−i2−i2i22i−2i−2i2i0000−2−22222−2−20000000000002−2−22i2−i2−i2i2000000000000
χ5922-2-2-2-2222-2-200002i2i2−i2−i2−i2−i2i2i200−2i2i2i−2i2-2-22i2−i2−i2i22i−2i−2i2i0000−2−22222−2−2000000000000−222−2−i2i2i2−i2000000000000
χ6022-2-2-2-2222-2-200002i2i2−i2−i2−i2−i2i2i200−2i2i2i−2i-222-2i2−i2−i2i2−2i2i2i−2i000022−2−2−2−222000000000000−222−2i2−i2−i2i2000000000000
χ6122-2-2-2-2222-2-200002−i2−i2i2i2i2i2−i2−i2002i−2i−2i2i2-2-22−i2i2i2−i2−2i2i2i−2i0000−2−22222−2−2000000000000−222−2i2−i2−i2i2000000000000
χ6222-2-2-2-2222-2-200002−i2−i2i2i2i2i2−i2−i2002i−2i−2i2i-222-2−i2i2i2−i22i−2i−2i2i000022−2−2−2−222000000000000−222−2−i2i2i2−i2000000000000
χ6322-2-2-2-2222-2-200002−i2−i2i2i2i2i2−i2−i200−2i2i2i−2i2-2-22−i2i2i2−i22i−2i−2i2i000022−2−2−2−2220000000000002−2−22i2−i2−i2i2000000000000
χ6422-2-2-2-2222-2-200002−i2−i2i2i2i2i2−i2−i200−2i2i2i−2i-222-2−i2i2i2−i2−2i2i2i−2i0000−2−22222−2−20000000000002−2−22−i2i2i2−i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-444-444-4-4-4000000004-4000000000000000000000000000000000000000000000000000000000000
χ6744-4-444-4-44-440000-42222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ6844-4-444-4-44-440000-4−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6944-4-4-4-444-4440000-42i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-4-4-444-4440000-4−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000002i2−2i222−222ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ724-44-44i−4i4i−4i000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000−2i22i2−2222−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ734-44-44i−4i4i−4i00000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000002i2−2i222−22−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ744-44-44i−4i4i−4i00000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000−2i22i2−22222ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ754-44-4−4i4i−4i4i000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000002i2−2i2−22222ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ764-44-4−4i4i−4i4i000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000−2i22i222−22−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ774-44-4−4i4i−4i4i00000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000002i2−2i2−2222−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ784-44-4−4i4i−4i4i00000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000000000000−2i22i222−222ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ794-4-444i−4i−4i4i0004i−4i4-400000000000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000
χ804-4-444i−4i−4i4i0004i−4i4-40000000000000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000
χ814-4-444i−4i−4i4i000−4i4i-4404ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ824-4-444i−4i−4i4i000−4i4i-440−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i0004i−4i-4404ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i0004i−4i-440−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ854-4-44−4i4i4i−4i000−4i4i4-400000000000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000
χ864-4-44−4i4i4i−4i000−4i4i4-40000000000000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000

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