Finite Group Databasebeta

← Group #128652

Character table — Group #128652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order1222444444444444888888882224448888888816161616161616164444448888881616161616161616161616161616161616161616888816161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1iiii−i−i−i−i-1-1111111-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1iiii−i−i−i−i-1-1-1-1-1-1111111ii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1−i−i−i−iiiii-1-1-1-1-1-1111111−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ17111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-1-111ii−i−iii−i−i-1-1ii−i−i11ii−i−ii−ii−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ18111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-1-111ii−i−iii−i−i-1-1−i−iii11−i−iiii−ii−iii−i−iii−i−i-1-111-1-111−ii−ii-11-11
χ19111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-1-111−i−iii−i−iii-1-1ii−i−i11ii−i−i−ii−ii−i−iii−i−iii-1-111-1-111i−ii−i-11-11
χ20111111111111-1-1-1-11111-1-1-1-111-111-1-1-1-1-1-1-111−i−iii−i−iii-1-1−i−iii11−i−iii−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ21111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iii−i−i11ii−i−i-1-1ii−i−ii−ii−i−i−iii−i−iii11-1-111-1-1−ii−ii-11-11
χ22111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iii−i−i11−i−iii-1-1−i−iiii−ii−i−i−iii−i−iii-1-111-1-111i−ii−i1-11-1
χ23111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−iii11ii−i−i-1-1ii−i−i−ii−iiii−i−iii−i−i-1-111-1-111−ii−ii1-11-1
χ24111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−iii11−i−iii-1-1−i−iii−ii−iiii−i−iii−i−i11-1-111-1-1i−ii−i-11-11
χ25111111111111-1-1-1-1-1-1-1-1111111-111-1111111-1-111-1-1-1-111-1-1ii−i−i-1-1−i−iii1-1-1111-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ26111111111111-1-1-1-1-1-1-1-1111111-111-1111111-1-111-1-1-1-111-1-1−i−iii-1-1ii−i−i1-1-1111-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ27111111111111-1-1-1-1-1-1-1-1111111-111-1111111-1-1-1-11111-1-1-1-1ii−i−i-1-1−i−iii-111-1-1-11111-1-1ii−i−i−i−iiii−i−iii−i−ii
χ28111111111111-1-1-1-1-1-1-1-1111111-111-1111111-1-1-1-11111-1-1-1-1−i−iii-1-1ii−i−i-111-1-1-11111-1-1−i−iiiii−i−i−iii−i−iii−i
χ29111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111ii−i−i11−i−iii1-1-11-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ30111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111−i−iii11ii−i−i1-1-11-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ31111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111ii−i−i11−i−iii-111-111-1-1-1-111ii−i−i−i−iii−iii−i−iii−i
χ32111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111−i−iii11ii−i−i-111-111-1-1-1-111−i−iiiii−i−ii−i−iii−i−ii
χ3322222222-2-2-2-222222222222200-200-2-2-20000-2-222222222000000000000-2-2-2-2000000000000000000000000
χ3422222222-2-2-2-222222222222200-200-2-2-20000-2-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ3522222222-2-2-2-22222-2-2-2-2-2-2-2-200-200-2220000222i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ3622222222-2-2-2-22222-2-2-2-2-2-2-2-200-200-222000022−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-2002002220000-2-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2002002220000-2-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222002002-2-200002222-2-2-2-222000000000000-222-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222002002-2-2000022-2-22222-2-20000000000002-2-22000000000000000000000000
χ412222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00200-22i−2i00002i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ422222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00200-22i−2i00002i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ432222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00200-2−2i2i0000−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ442222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00200-2−2i2i0000−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ452222-2-2-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-2002−2i2i00002i−2i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ462222-2-2-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-2002−2i2i00002i−2i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ472222-2-2-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20022i−2i0000−2i2i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ482222-2-2-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20022i−2i0000−2i2i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ492222-2-2-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i22-2-2-22−2i2i2i2i−2i−2i−2i2i000000002-200002i−2i00000000000000000000000000000000
χ502222-2-2-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2222−2i2i−2i−2i2i2i−2i2i00000000-220000−2i2i00000000000000000000000000000000
χ512222-2-2-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-222i−2i−2i−2i2i2i2i−2i000000002-20000−2i2i00000000000000000000000000000000
χ522222-2-2-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i-2-2-22222i−2i2i2i−2i−2i2i−2i00000000-2200002i−2i00000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i222-2-2-22i−2i−2i−2i2i2i−2i2i00000000-2200002i−2i00000000000000000000000000000000
χ542222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i-2-2222-22i−2i2i2i−2i−2i−2i2i000000002-20000−2i2i00000000000000000000000000000000
χ552222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i222-2-2-2−2i2i2i2i−2i−2i2i−2i00000000-220000−2i2i00000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i-2-2222-2−2i2i−2i−2i2i2i2i−2i000000002-200002i−2i00000000000000000000000000000000
χ5722-2-222-2-200002i−2i2i−2i2i−2i2i−2i2-22-2000000000000002-22i−2i2i−2i2-2001+i−1−i1−i−1+i001−i−1+i1+i−1−i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ5822-2-222-2-200002i−2i2i−2i2i−2i2i−2i2-22-2000000000000002-22i−2i2i−2i2-200−1−i1+i−1+i1−i00−1+i1−i−1−i1+i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ5922-2-222-2-200002i−2i2i−2i2i−2i2i−2i2-22-200000000000000-22−2i2i−2i2i-22001+i−1−i1−i−1+i001−i−1+i1+i−1−i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ6022-2-222-2-200002i−2i2i−2i2i−2i2i−2i2-22-200000000000000-22−2i2i−2i2i-2200−1−i1+i−1+i1−i00−1+i1−i−1−i1+i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ6122-2-222-2-200002i−2i2i−2i−2i2i−2i2i-22-22000000000000002i−2i-222-2−2i2i001+i−1−i1−i−1+i00−1+i1−i−1−i1+i0000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ6222-2-222-2-200002i−2i2i−2i−2i2i−2i2i-22-22000000000000002i−2i-222-2−2i2i00−1−i1+i−1+i1−i001−i−1+i1+i−1−i000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ6322-2-222-2-200002i−2i2i−2i−2i2i−2i2i-22-2200000000000000−2i2i2-2-222i−2i001+i−1−i1−i−1+i00−1+i1−i−1−i1+i000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ6422-2-222-2-200002i−2i2i−2i−2i2i−2i2i-22-2200000000000000−2i2i2-2-222i−2i00−1−i1+i−1+i1−i001−i−1+i1+i−1−i0000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ6522-2-222-2-20000−2i2i−2i2i2i−2i2i−2i-22-22000000000000002i−2i2-2-22−2i2i001−i−1+i1+i−1−i00−1−i1+i−1+i1−i000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ6622-2-222-2-20000−2i2i−2i2i2i−2i2i−2i-22-22000000000000002i−2i2-2-22−2i2i00−1+i1−i−1−i1+i001+i−1−i1−i−1+i0000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ6722-2-222-2-20000−2i2i−2i2i2i−2i2i−2i-22-2200000000000000−2i2i-222-22i−2i001−i−1+i1+i−1−i00−1−i1+i−1+i1−i0000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ6822-2-222-2-20000−2i2i−2i2i2i−2i2i−2i-22-2200000000000000−2i2i-222-22i−2i00−1+i1−i−1−i1+i001+i−1−i1−i−1+i000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ6922-2-222-2-20000−2i2i−2i2i−2i2i−2i2i2-22-2000000000000002-2−2i2i−2i2i2-2001−i−1+i1+i−1−i001+i−1−i1−i−1+i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ7022-2-222-2-20000−2i2i−2i2i−2i2i−2i2i2-22-2000000000000002-2−2i2i−2i2i2-200−1+i1−i−1−i1+i00−1−i1+i−1+i1−i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ7122-2-222-2-20000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000-222i−2i2i−2i-22001−i−1+i1+i−1−i001+i−1−i1−i−1+i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ7222-2-222-2-20000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000-222i−2i2i−2i-2200−1+i1−i−1−i1+i00−1−i1+i−1+i1−i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ7344-4-4-4-44400004i−4i−4i4i4-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4-44400004i−4i−4i4i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-4440000−4i4i4i−4i4-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-4440000−4i4i4i−4i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i4i−4i4-4000000000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000000000
χ784-44-44i−4i4i−4i4i−4i4-400000000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000000000
χ794-44-44i−4i4i−4i−4i4i-440000000000004-404i−4i000000000000000000000000000000000000000000000000000000000
χ804-44-44i−4i4i−4i−4i4i-44000000000000-440−4i4i000000000000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i4i−4i-440000000000004-40−4i4i000000000000000000000000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i4i−4i-44000000000000-4404i−4i000000000000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i−4i4i4-4000000000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i−4i4i4-400000000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000000000
χ858-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000

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