Finite Group Databasebeta

← Group #111199

Character table — Group #111199

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12224444224444444444444422444488888888888888884444444488888888888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ9111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i
χ10111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111-11-11−i−iii
χ11111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii−i−i−i−iiiii-1-1-1-11111-11-11ii−i−i
χ12111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii
χ13111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1-11-11−i−iii
χ14111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−i−i−iiiii-1-1-1-111111-11-1ii−i−i
χ15111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-111111-11-1−i−iii
χ16111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1-11-11ii−i−i
χ171111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−i1-1-11i−ii−i
χ181111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111i−ii−ii−ii−i11-1-111-1-1−i−iii−i−iii-111-1−ii−ii
χ191111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1i−ii−i−ii−ii-1-111-1-111−i−iii−i−iii-111-1i−ii−i
χ201111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i1-1-11−ii−ii
χ211111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−ii−iii−ii−i-1-111-1-111ii−i−iii−i−i-111-1−ii−ii
χ221111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i-1-111-1-111−i−iii−i−iii1-1-11i−ii−i
χ231111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii1-1-11−ii−ii
χ241111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111−ii−ii−ii−ii11-1-111-1-1ii−i−iii−i−i-111-1i−ii−i
χ251111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iiii−i−ii1-1-11−i−iiiii−i−i−i−iiiii−i−i-1-111-111-1
χ261111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−ii−i−ii1-1-11−i−iiiii−i−iii−i−i−i−iii11-1-11-1-11
χ271111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iiii−i−ii-111-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-111-1
χ281111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−ii−i−ii-111-1ii−i−i−i−iii−i−iiiii−i−i-1-1111-1-11
χ291111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii−iii−i1-1-11ii−i−i−i−iii−i−iiiii−i−i11-1-11-1-11
χ301111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i−iii−i1-1-11ii−i−i−i−iiiii−i−i−i−iii-1-111-111-1
χ311111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii−iii−i-111-1−i−iiiii−i−iii−i−i−i−iii-1-1111-1-11
χ321111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i−iii−i-111-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-111-1
χ332222222222-2-22222-2-2222222-2-2-2-2-2-20000000022222222000000000000-2-2-2-2000000000000000000000000
χ342222222222-2-22222-2-2222222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ362222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ3722222222-2-22222-2-222-2-222-2-2-22-2-22-22222-2-2-2-20000000000000000-2-2220000000000000000000000000000
χ3822222222-2-22222-2-222-2-222-2-2-22-2-22-2-2-2-2-22222000000000000000022-2-20000000000000000000000000000
χ3922222222-2-222-2-2-2-22222-2-2222-2-2-2-22222222220000000000000000-2-2-2-20000000000000000000000000000
χ4022222222-2-222-2-2-2-22222-2-2222-2-2-2-22-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000000000
χ4122222222-2-2-2-222-2-2-2-2-2-222-2-22-222-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4222222222-2-2-2-222-2-2-2-2-2-222-2-22-222-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-222-22222-2000000000000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-222-22222-200000000000000000000000000000000-22-222-22-20000000000000000
χ452222-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-2222000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ462222-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-222200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2-222-2-2222222-22-2-20000000022-2-2-2-222000000000000-222-2000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2-222-2-2222222-22-2-200000000-2-22222-2-20000000000002-2-22000000000000000000000000
χ492222-2-2-2-2-2-2222222-2-2-2-2-2-222-22-22-222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i0000000000000000000000000000
χ502222-2-2-2-2-2-2222222-2-2-2-2-2-222-22-22-22−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i0000000000000000000000000000
χ512222-2-2-2-2-2-222-2-222-2-22222-2-22-2-222-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i0000000000000000000000000000
χ522222-2-2-2-2-2-222-2-222-2-22222-2-22-2-222-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i0000000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-2222-22-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-2-2-2222-22-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552222-2-2-2-2-2-2-2-2-2-222222222-2-2-222-2-22000000000000000000000000000000002-2-22-222-20000000000000000
χ562222-2-2-2-2-2-2-2-2-2-222222222-2-2-222-2-2200000000000000000000000000000000-222-22-2-220000000000000000
χ5722-2-22i2i−2i−2i2-2002i−2i2i−2i002i−2i2-22-2000000000000002-22i−2i2i−2i2-21−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ5822-2-22i2i−2i−2i2-2002i−2i2i−2i002i−2i2-22-2000000000000002-22i−2i2i−2i2-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ5922-2-22i2i−2i−2i2-2002i−2i2i−2i002i−2i2-22-200000000000000-22−2i2i−2i2i-221−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ6022-2-22i2i−2i−2i2-2002i−2i2i−2i002i−2i2-22-200000000000000-22−2i2i−2i2i-22−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ6122-2-22i2i−2i−2i2-200−2i2i2i−2i00−2i2i-22-22000000000000002i−2i-222-2−2i2i1+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ6222-2-22i2i−2i−2i2-200−2i2i2i−2i00−2i2i-22-22000000000000002i−2i-222-2−2i2i−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ6322-2-22i2i−2i−2i2-200−2i2i2i−2i00−2i2i-22-2200000000000000−2i2i2-2-222i−2i1+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ6422-2-22i2i−2i−2i2-200−2i2i2i−2i00−2i2i-22-2200000000000000−2i2i2-2-222i−2i−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ6522-2-2−2i−2i2i2i2-2002i−2i−2i2i002i−2i-22-22000000000000002i−2i2-2-22−2i2i1−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ6622-2-2−2i−2i2i2i2-2002i−2i−2i2i002i−2i-22-22000000000000002i−2i2-2-22−2i2i−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ6722-2-2−2i−2i2i2i2-2002i−2i−2i2i002i−2i-22-2200000000000000−2i2i-222-22i−2i1−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ6822-2-2−2i−2i2i2i2-2002i−2i−2i2i002i−2i-22-2200000000000000−2i2i-222-22i−2i−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ6922-2-2−2i−2i2i2i2-200−2i2i−2i2i00−2i2i2-22-2000000000000002-2−2i2i−2i2i2-21+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ7022-2-2−2i−2i2i2i2-200−2i2i−2i2i00−2i2i2-22-2000000000000002-2−2i2i−2i2i2-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ7122-2-2−2i−2i2i2i2-200−2i2i−2i2i00−2i2i2-22-200000000000000-222i−2i2i−2i-221+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ7222-2-2−2i−2i2i2i2-200−2i2i−2i2i00−2i2i2-22-200000000000000-222i−2i2i−2i-22−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ7344-4-44i4i−4i−4i-44004i−4i−4i4i00−4i4i4-4-4400000000000000000000000000000000000000000000000000000000000000
χ7444-4-44i4i−4i−4i-4400−4i4i−4i4i004i−4i-444-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4−4i−4i4i4i-44004i−4i4i−4i00−4i4i-444-400000000000000000000000000000000000000000000000000000000000000
χ7644-4-4−4i−4i4i4i-4400−4i4i4i−4i004i−4i4-4-4400000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i004-400004i−4i00000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000
χ784-44-44i−4i4i−4i004-400004i−4i0000000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000
χ794-44-44i−4i4i−4i00-440000−4i4i0000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000000000
χ804-44-44i−4i4i−4i00-440000−4i4i000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i004-40000−4i4i00000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i004-40000−4i4i0000000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i00-4400004i−4i0000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i00-4400004i−4i000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000000000
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.