Finite Group Databasebeta

← Group #369490

Character table — Group #369490

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222444444444444444444444444888888888888888888888888888888888888161616161616
order12224444222222444444222244444444888888888888444444888888888888888888888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1111111-1-1-1-1
χ171111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-11-111-1-11-1i−i1-1
χ181111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1ii−i−iiiii−i−i−i−i-1-11111-1-1i−iii−i−iii−i−i−i−iii−i−iii−i−iii11-1-1-11-1-111-11−ii-11
χ191111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1ii−i−i−i−i−i−iiiii11-1-1-1-111i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-1111-111-1-1-11i−i-11
χ201111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1ii−i−i−i−i−i−iiiii-1-111-1-111i−i−i−iiiii−i−iii−i−iii−i−i−i−iii-1-111-11-1-1111-1−ii1-1
χ211111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1−i−iiiiiii−i−i−i−i11-1-1-1-111−iiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-1111-111-1-1-11−ii-11
χ221111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1−i−iiiiiii−i−i−i−i-1-111-1-111−iiii−i−i−i−iii−i−iii−i−iiiii−i−i-1-111-11-1-1111-1i−i1-1
χ231111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1−ii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-11-111-1-11-1−ii1-1
χ241111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1−i−iii−i−i−i−iiiii-1-11111-1-1−ii−i−iii−i−iiiii−i−iii−i−iii−i−i11-1-1-11-1-111-11i−i-11
χ251111-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iiiii−i−i−i−i11-1-1-1-111i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-11-1-1-111-11−ii1-1
χ261111-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iiiii−i−i−i−i-1-111-1-111i−i−i−iii−i−iii−i−iiiii−i−i−i−iii11-1-1-1111-1-11-1i−i-11
χ271111-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−i−i−i−i−iiiii11-1-111-1-1i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-1-1111-1-1-1111-1−ii-11
χ281111-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−i−i−i−i−iiiii-1-11111-1-1i−iii−i−i−i−iiiii−i−i−i−iii−i−iii-1-111-1111-1-1-11i−i1-1
χ291111-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iiiiiii−i−i−i−i11-1-111-1-1−ii−i−iiiii−i−iii−i−i−i−iii−i−iii-1-1111-1-1-1111-1i−i-11
χ301111-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iiiiiii−i−i−i−i-1-11111-1-1−ii−i−iiiii−i−i−i−iiiii−i−iii−i−i-1-111-1111-1-1-11−ii1-1
χ311111-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−i−i−iiiii11-1-1-1-111−iiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-11-1-1-111-11i−i1-1
χ321111-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−i−i−iiiii-1-111-1-111−iiii−i−iii−i−iii−i−i−i−iiiii−i−i11-1-1-1111-1-11-1−ii-11
χ3322222222-2-22-22-22-2-2-22-200000000000022-2-222-2-22222000000000000002-22-2000000000000-2-20000000000
χ3422222222-2-22-22-22-2-2-22-200000000000022-2-222-2-2-2-2-2-200000000000000-22-22000000000000220000000000
χ3522222222-2-22-22-22-2-2-22-2000000000000-2-222-2-222222200000000000000-22-22000000000000-2-20000000000
χ3622222222-2-22-22-22-2-2-22-2000000000000-2-222-2-222-2-2-2-2000000000000002-22-2000000000000220000000000
χ3722222222-2-2-22-22-22-2-2-2222-2-2-2-22222220000000000000000-2-200002-22-20000000000000000000000000000
χ3822222222-2-2-22-22-22-2-2-2222-2-2-2-222-2-2-2-20000000000000000220000-22-220000000000000000000000000000
χ3922222222-2-2-22-22-22-2-2-22-2-22222-2-222220000000000000000-2-20000-22-220000000000000000000000000000
χ4022222222-2-2-22-22-22-2-2-22-2-22222-2-2-2-2-2-200000000000000002200002-22-20000000000000000000000000000
χ412222-2-2-2-2-2-22-22-2-2222-222222-2-2-2-22i2i−2i−2i0000000000000000−2i2i00002i−2i−2i2i0000000000000000000000000000
χ422222-2-2-2-2-2-22-22-2-2222-222222-2-2-2-2−2i−2i2i2i00000000000000002i−2i0000−2i2i2i−2i0000000000000000000000000000
χ432222-2-2-2-2-2-22-22-2-2222-22-2-2-2-222222i2i−2i−2i0000000000000000−2i2i0000−2i2i2i−2i0000000000000000000000000000
χ442222-2-2-2-2-2-22-22-2-2222-22-2-2-2-22222−2i−2i2i2i00000000000000002i−2i00002i−2i−2i2i0000000000000000000000000000
χ452222-2-2-2-2-2-2-22-222-2222-20000000000002i2i−2i−2i−2i−2i2i2i22-2-2000000000000002i−2i−2i2i000000000000-220000000000
χ462222-2-2-2-2-2-2-22-222-2222-20000000000002i2i−2i−2i−2i−2i2i2i-2-22200000000000000−2i2i2i−2i0000000000002-20000000000
χ472222-2-2-2-2-2-2-22-222-2222-2000000000000−2i−2i2i2i2i2i−2i−2i22-2-200000000000000−2i2i2i−2i000000000000-220000000000
χ482222-2-2-2-2-2-2-22-222-2222-2000000000000−2i−2i2i2i2i2i−2i−2i-2-222000000000000002i−2i−2i2i0000000000002-20000000000
χ4922-2-222-2-22-222-2-2222-2-2-22-22-22-22-200002-22-22-22-200000000002-22-200000000000000000000000000000000
χ5022-2-222-2-22-222-2-2222-2-2-22-22-22-22-20000-22-22-22-220000000000-22-2200000000000000000000000000000000
χ5122-2-222-2-22-222-2-2222-2-2-2-22-22-22-2200002-22-22-22-20000000000-22-2200000000000000000000000000000000
χ5222-2-222-2-22-222-2-2222-2-2-2-22-22-22-220000-22-22-22-2200000000002-22-200000000000000000000000000000000
χ5322-2-222-2-2-222-2-222-2-22-220000000000002-2-222-2-2200000000000000000000002i−2i2i−2i00000000002i−2i2i−2i000000
χ5422-2-222-2-2-222-2-222-2-22-220000000000002-2-222-2-220000000000000000000000−2i2i−2i2i0000000000−2i2i−2i2i000000
χ5522-2-222-2-2-222-2-222-2-22-22000000000000-222-2-222-200000000000000000000002i−2i2i−2i0000000000−2i2i−2i2i000000
χ5622-2-222-2-2-222-2-222-2-22-22000000000000-222-2-222-20000000000000000000000−2i2i−2i2i00000000002i−2i2i−2i000000
χ5722-2-222-2-2-22-222-2-22-222-22-2-22-222-200000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i000000000000
χ5822-2-222-2-2-22-222-2-22-222-22-2-22-222-20000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i000000000000
χ5922-2-222-2-2-22-222-2-22-222-2-222-22-2-2200000000000000002i−2i2i−2i0000000000000000000000−2i2i−2i2i000000000000
χ6022-2-222-2-2-22-222-2-22-222-2-222-22-2-220000000000000000−2i2i−2i2i00000000000000000000002i−2i2i−2i000000000000
χ6122-2-2-2-2222-2-2-22222-22-2-22-2-222-2-2200002i−2i2i−2i−2i2i−2i2i00000000002i−2i−2i2i00000000000000000000000000000000
χ6222-2-2-2-2222-2-2-22222-22-2-22-2-222-2-220000−2i2i−2i2i2i−2i2i−2i0000000000−2i2i2i−2i00000000000000000000000000000000
χ6322-2-2-2-2222-2-2-22222-22-2-2-222-2-222-200002i−2i2i−2i−2i2i−2i2i0000000000−2i2i2i−2i00000000000000000000000000000000
χ6422-2-2-2-2222-2-2-22222-22-2-2-222-2-222-20000−2i2i−2i2i2i−2i2i−2i00000000002i−2i−2i2i00000000000000000000000000000000
χ6522-2-2-2-222-222-2-22-222-22-22-22-2-22-2200000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i000000000000
χ6622-2-2-2-222-222-2-22-222-22-22-22-2-22-220000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000000000
χ6722-2-2-2-222-222-2-22-222-22-2-22-222-22-200000000000000002i−2i−2i2i0000000000000000000000−2i2i2i−2i000000000000
χ6822-2-2-2-222-222-2-22-222-22-2-22-222-22-20000000000000000−2i2i2i−2i00000000000000000000002i−2i−2i2i000000000000
χ6922-2-2-2-222-22-222-22-22-2-220000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000002-2-220000000000−2i2i2i−2i000000
χ7022-2-2-2-222-22-222-22-22-2-220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000-222-200000000002i−2i−2i2i000000
χ7122-2-2-2-222-22-222-22-22-2-22000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000002-2-2200000000002i−2i−2i2i000000
χ7222-2-2-2-222-22-222-22-22-2-22000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000-222-20000000000−2i2i2i−2i000000
χ734444444444-4-4-4-4-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-44-4-4-444-4-44-444000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-4444-444-4-4-4-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i000000000000000000002+2i−2−2i2−2i−2+2i000000002i2−2i222−2200000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ784-44-44i−4i4i−4i000000000000000000002+2i−2−2i2−2i−2+2i00000000−2i22i2−22220000000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ794-44-44i−4i4i−4i00000000000000000000−2−2i2+2i−2+2i2−2i000000002i2−2i222−220000000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ804-44-44i−4i4i−4i00000000000000000000−2−2i2+2i−2+2i2−2i00000000−2i22i2−222200000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ814-44-4−4i4i−4i4i000000000000000000002−2i−2+2i2+2i−2−2i000000002i2−2i2−222200000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ824-44-4−4i4i−4i4i000000000000000000002−2i−2+2i2+2i−2−2i00000000−2i22i222−220000000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ834-44-4−4i4i−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i000000002i2−2i2−22220000000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ844-44-4−4i4i−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i00000000−2i22i222−2200000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000
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.