Finite Group Databasebeta

← Group #106943

Character table — Group #106943

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12224444222244444444444422222444444444224444444444888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ81111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1111-1-1-11-11-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1111-1-1-11-11-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1111-1-1-11-11-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1111-1-1-11-11-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-11-1-111-1-11-11iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-11-1-111-1-11-11iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-11-1-111-1-11-11−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-11-1-111-1-11-11−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii
χ171111-1-1-1-111-1-111-1-11111-1-1-1-1-111-1-11-1-11-1-1111-111-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−i
χ181111-1-1-1-111-1-111-1-11111-1-1-1-1-111-1-11-1-11-1-1111-111-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii
χ191111-1-1-1-111-1-111-1-11111-1-1-1-1-111-1-11-1-11-1-1111-111-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111−ii−ii
χ201111-1-1-1-111-1-111-1-11111-1-1-1-1-111-1-11-1-11-1-1111-111-1-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111i−ii−i
χ211111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-1111-1-111-1-1111-1-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−ii
χ221111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-1111-1-111-1-1111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i
χ231111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-1111-1-111-1-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1i−ii−i
χ241111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-1111-1-111-1-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−ii−ii
χ251111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-111-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-111-1
χ261111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-111-1-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii1-1-11
χ271111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-111-1-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i1-1-11
χ281111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-111-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-111-1
χ291111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1111111-111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i1-1-11
χ301111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1111111-111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1
χ311111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1111111-111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1
χ321111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1111111-111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii1-1-11
χ33222222222222-2-2-2-2-2-22222-2-220000-2-2-220000-2000000000000000000002-22-22-22-200000000000000000000
χ34222222222222-2-2-2-2-2-22222-2-220000-2-2-220000-200000000000000000000-22-22-22-2200000000000000000000
χ352222222222-2-22222-2-2-2-222-2-2-222-2-2-2-22-222-2-22-22-2200000000000000000000000000000000000000000000
χ362222222222-2-22222-2-2-2-222-2-2-2-2-222-2-22-2-2-22222-22-200000000000000000000000000000000000000000000
χ372222222222-2-2-2-2-2-222-2-22222-2000022-2-20000-20000000000002-22-22-22-20000000000000000000000000000
χ382222222222-2-2-2-2-2-222-2-22222-2000022-2-20000-2000000000000-22-22-22-220000000000000000000000000000
χ3922222222-2-22222222222-2-222-22222-2-2-2-22222-2-2-2-2-200000000000000000000000000000000000000000000
χ4022222222-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ4122222222-2-222-2-2-2-2-2-222-2-2-2-2-20000222-2000020000000000002-22-2-22-220000000000000000000000000000
χ4222222222-2-222-2-2-2-2-2-222-2-2-2-2-20000222-200002000000000000-22-222-22-20000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-222-2-2-2-22220000-2-22200002000000000000000000002-22-2-22-2200000000000000000000
χ4422222222-2-2-2-2-2-2-2-222-2-2-2-22220000-2-2220000200000000000000000000-22-222-22-200000000000000000000
χ452222-2-2-2-2222222-2-2-2-2-2-2-2-22222222-22-2-2-2-2-2-2222-2-200000000000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-2-2-2222-2-2-2-2-22-2-222222-2-22200000000000000000000000000000000000000000000
χ472222-2-2-2-22222-2-22222-2-2-2-2-2-2200002-22-20000-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ482222-2-2-2-22222-2-22222-2-2-2-2-2-2200002-22-20000-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ492222-2-2-2-222-2-2-2-222-2-222-2-222-20000-22220000-2000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ502222-2-2-2-222-2-2-2-222-2-222-2-222-20000-22220000-200000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ512222-2-2-2-2-2-222-2-22222-2-222-2-2-20000-22-2200002000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ522222-2-2-2-2-2-222-2-22222-2-222-2-2-20000-22-220000200000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ532222-2-2-2-2-2-2-2-222-2-2222222-2-2222-2-2-222-2-2-222-22-2-2200000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-222-2-2222222-2-22-2-222-222-222-2-2-2-222-200000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2-2-222-2-2222222200002-2-2-2000020000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-222-2-2222222200002-2-2-200002000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ5722-2-22i2i−2i−2i002-22-22i−2i2i−2i2i−2i002-202-22-200002i−2i2i−2i000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ5822-2-22i2i−2i−2i002-22-22i−2i2i−2i2i−2i002-202-22-200002i−2i2i−2i00000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ5922-2-22i2i−2i−2i002-22-22i−2i2i−2i2i−2i002-20-22-220000−2i2i−2i2i000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ6022-2-22i2i−2i−2i002-22-22i−2i2i−2i2i−2i002-20-22-220000−2i2i−2i2i00000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ6122-2-22i2i−2i−2i00-222-22i−2i−2i2i−2i2i00-2202-2-2200002i−2i−2i2i000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ6222-2-22i2i−2i−2i00-222-22i−2i−2i2i−2i2i00-2202-2-2200002i−2i−2i2i00000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ6322-2-22i2i−2i−2i00-222-22i−2i−2i2i−2i2i00-220-222-20000−2i2i2i−2i000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ6422-2-22i2i−2i−2i00-222-22i−2i−2i2i−2i2i00-220-222-20000−2i2i2i−2i00000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ6522-2-2−2i−2i2i2i002-22-2−2i2i−2i2i−2i2i002-202-22-20000−2i2i−2i2i000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ6622-2-2−2i−2i2i2i002-22-2−2i2i−2i2i−2i2i002-202-22-20000−2i2i−2i2i00000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ6722-2-2−2i−2i2i2i002-22-2−2i2i−2i2i−2i2i002-20-22-2200002i−2i2i−2i000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ6822-2-2−2i−2i2i2i002-22-2−2i2i−2i2i−2i2i002-20-22-2200002i−2i2i−2i00000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ6922-2-2−2i−2i2i2i00-222-2−2i2i2i−2i2i−2i00-2202-2-220000−2i2i2i−2i000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ7022-2-2−2i−2i2i2i00-222-2−2i2i2i−2i2i−2i00-2202-2-220000−2i2i2i−2i00000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ7122-2-2−2i−2i2i2i00-222-2−2i2i2i−2i2i−2i00-220-222-200002i−2i−2i2i000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ7222-2-2−2i−2i2i2i00-222-2−2i2i2i−2i2i−2i00-220-222-200002i−2i−2i2i00000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ7344-4-44i4i−4i−4i004-4-44−4i4i−4i4i4i−4i00-4400000000000000000000000000000000000000000000000000000000000000
χ7444-4-44i4i−4i−4i00-44-44−4i4i4i−4i−4i4i004-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4−4i−4i4i4i004-4-444i−4i4i−4i−4i4i00-4400000000000000000000000000000000000000000000000000000000000000
χ7644-4-4−4i−4i4i4i00-44-444i−4i−4i4i4i−4i004-400000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i4-400000000004i−4i000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ784-44-44i−4i4i−4i4-400000000004i−4i00000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ794-44-44i−4i4i−4i-440000000000−4i4i000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000
χ804-44-44i−4i4i−4i-440000000000−4i4i00000000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000
χ814-44-4−4i4i−4i4i4-40000000000−4i4i000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ824-44-4−4i4i−4i4i4-40000000000−4i4i00000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ834-44-4−4i4i−4i4i-4400000000004i−4i000000000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000
χ844-44-4−4i4i−4i4i-4400000000004i−4i00000000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000
χ858-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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