Finite Group Databasebeta

← Group #106932

Character table — Group #106932

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12224444224444444444444422224444444444888888882444888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1111-1-1-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-1-1iiii−i−i−i−i11-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ1111111111-1-111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111
χ1211111111-1-111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-1111-1-11111-1iiii−i−i−i−i-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-1111-1-11111-1iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-1111-1-11111-1−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-111-1-1-1-1-1-111-1-1-1-11-1-1-1111-1-11111-1−i−i−i−iiiii-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111
χ171111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-11ii−i−iii−i−i-111-111-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-11ii−i−iii−i−i-111-1-1-111-1-111i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ191111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-11−i−iii−i−iii-111-111-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ201111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-11−i−iii−i−iii-111-1-1-111-1-111−ii−ii−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1111ii−i−iii−i−i1-1-1111-1-111-1-1i−ii−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii
χ221111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1111ii−i−iii−i−i1-1-11-1-111-1-111i−ii−i−i−iii−i−iii11-1-111-1-1−ii−iii−ii−i
χ231111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1111−i−iii−i−iii1-1-1111-1-111-1-1−ii−iiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i
χ241111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1111−i−iii−i−iii1-1-11-1-111-1-111−ii−iiii−i−iii−i−i11-1-111-1-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-111-1-11111-1-1-1-111-111111-1-1-1-1-111-111-1-1-1-111-11-11ii−i−i−i−iii1-1-1111-1-1-1-111ii−i−i−i−iii−iii−i−iii−i
χ261111-1-1-1-1-1-111-1-11111-1-1-1-111-111111-1-1-1-1-111-111-1-1-1-111-11-11−i−iiiii−i−i1-1-1111-1-1-1-111−i−iiiii−i−ii−i−iii−i−ii
χ271111-1-1-1-1-1-111-1-11111-1-1-1-111-111111-1-1-1-1-111-1-1-11111-1-1-11-11ii−i−i−i−iii-111-1-1-11111-1-1ii−i−i−i−iiii−i−iii−i−ii
χ281111-1-1-1-1-1-111-1-11111-1-1-1-111-111111-1-1-1-1-111-1-1-11111-1-1-11-11−i−iiiii−i−i-111-1-1-11111-1-1−i−iiiii−i−i−iii−i−iii−i
χ291111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-11111-1-1-111-1-1-1-1111-11-1ii−i−i−i−iii1-1-11-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ301111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-11111-1-1-111-1-1-1-1111-11-1−i−iiiii−i−i1-1-11-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ311111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-11111-1-1-1-1-11111-1-11-11-1ii−i−i−i−iii-111-111-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ321111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-11111-1-1-1-1-11111-1-11-11-1−i−iiiii−i−i-111-111-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ332222222222222222-2-222-2-222-2-222-2-2-2222222-200000000-2-2-2-2000000000000000000000000000000000000
χ342222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ352222222222-2-2-2-22222-2-222-2-2-2-2002-22000000-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ362222222222-2-2-2-22222-2-222-2-2-2-2002-22000000-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ372222222222-2-2-2-222-2-2-2-2-2-2-2-22200-22-200000022i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ382222222222-2-2-2-222-2-2-2-2-2-2-2-22200-22-20000002−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ3922222222-2-222-2-2-2-2222222-2-2-2222-2-2-222-2-2-2-2200000000-2-222000000000000000000000000000000000000
χ4022222222-2-222-2-2-2-2222222-2-2-22-2-2-2-2-2-2-2222220000000022-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-222-2-222222-200-22-2000000-222222222000000000000-2-2-2-2000000000000000000000000
χ4222222222-2-2-2-222-2-222-2-222222-200-22-2000000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ4322222222-2-2-2-222-2-2-2-2-2-2-2-222-22002-2200000020000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-2-222-2-2-2-2-2-2-2-222-22002-220000002000000000000000000000000-22-222-22-20000000000000000
χ452222-2-2-2-2222222-2-222-2-2-2-2-2-22222-2-22-2-222-2-2-2000000002-2-22000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-222-2-2-2-2-2-222-2-2-2-2222-2-222-200000000-222-2000000000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2-22222-2-222-2-200-222000000222-2-2-2-222000000000000-222-2000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2-22222-2-222-2-200-2220000002-2-22222-2-20000000000002-2-22000000000000000000000000
χ492222-2-2-2-222-2-2-2-2-2-2-2-222222222002-2-2000000-20000000000000000000000002-2-222-2-220000000000000000
χ502222-2-2-2-222-2-2-2-2-2-2-2-222222222002-2-2000000-2000000000000000000000000-222-2-222-20000000000000000
χ512222-2-2-2-2-2-222-2-222-2-2-2-222222-222-2-22-2-2-2-2222000000002-22-2000000000000000000000000000000000000
χ522222-2-2-2-2-2-222-2-222-2-2-2-222222-2-2-2-2-222222-2-2200000000-22-22000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-222222222-2-2-2-22-2002-2-200000020000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ542222-2-2-2-2-2-2-2-222222222-2-2-2-22-2002-2-20000002000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-22222-2-2-2200-222000000-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-22222-2-2-2200-222000000-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ5722-2-22i−2i2i−2i2-22-22-22i−2i002i−2i002i−2i002-20002i−2i2-22i−2i0000000000000i2−i22−2i2−i22−2000000000000i2−i22−2i2−i22−200000000
χ5822-2-22i−2i2i−2i2-22-22-22i−2i002i−2i002i−2i002-20002i−2i2-22i−2i0000000000000−i2i2−22−i2i2−22000000000000−i2i2−22−i2i2−2200000000
χ5922-2-22i−2i2i−2i2-22-22-22i−2i002i−2i002i−2i00-22000−2i2i-22−2i2i0000000000000i2−i22−2i2−i22−2000000000000−i2i2−22−i2i2−2200000000
χ6022-2-22i−2i2i−2i2-22-22-22i−2i002i−2i002i−2i00-22000−2i2i-22−2i2i0000000000000−i2i2−22−i2i2−22000000000000i2−i22−2i2−i22−200000000
χ6122-2-22i−2i2i−2i-222-2-22−2i2i002i−2i00−2i2i002-20002i−2i-22−2i2i00000000000002−2−i2i2−22i2−i20000000000002−2−i2i2−22i2−i200000000
χ6222-2-22i−2i2i−2i-222-2-22−2i2i002i−2i00−2i2i002-20002i−2i-22−2i2i0000000000000−22i2−i22−2−i2i2000000000000−22i2−i22−2−i2i200000000
χ6322-2-22i−2i2i−2i-222-2-22−2i2i002i−2i00−2i2i00-22000−2i2i2-22i−2i00000000000002−2−i2i2−22i2−i2000000000000−22i2−i22−2−i2i200000000
χ6422-2-22i−2i2i−2i-222-2-22−2i2i002i−2i00−2i2i00-22000−2i2i2-22i−2i0000000000000−22i2−i22−2−i2i20000000000002−2−i2i2−22i2−i200000000
χ6522-2-2−2i2i−2i2i2-22-22-2−2i2i00−2i2i00−2i2i002-2000−2i2i2-2−2i2i0000000000000i2−i2−22i2−i2−22000000000000i2−i2−22i2−i2−2200000000
χ6622-2-2−2i2i−2i2i2-22-22-2−2i2i00−2i2i00−2i2i002-2000−2i2i2-2−2i2i0000000000000−i2i22−2−i2i22−2000000000000−i2i22−2−i2i22−200000000
χ6722-2-2−2i2i−2i2i2-22-22-2−2i2i00−2i2i00−2i2i00-220002i−2i-222i−2i0000000000000i2−i2−22i2−i2−22000000000000−i2i22−2−i2i22−200000000
χ6822-2-2−2i2i−2i2i2-22-22-2−2i2i00−2i2i00−2i2i00-220002i−2i-222i−2i0000000000000−i2i22−2−i2i22−2000000000000i2−i2−22i2−i2−2200000000
χ6922-2-2−2i2i−2i2i-222-2-222i−2i00−2i2i002i−2i002-2000−2i2i-222i−2i00000000000002−2i2−i2−22−i2i20000000000002−2i2−i2−22−i2i200000000
χ7022-2-2−2i2i−2i2i-222-2-222i−2i00−2i2i002i−2i002-2000−2i2i-222i−2i0000000000000−22−i2i22−2i2−i2000000000000−22−i2i22−2i2−i200000000
χ7122-2-2−2i2i−2i2i-222-2-222i−2i00−2i2i002i−2i00-220002i−2i2-2−2i2i00000000000002−2i2−i2−22−i2i2000000000000−22−i2i22−2i2−i200000000
χ7222-2-2−2i2i−2i2i-222-2-222i−2i00−2i2i002i−2i00-220002i−2i2-2−2i2i0000000000000−22−i2i22−2i2−i20000000000002−2i2−i2−22−i2i200000000
χ7344-4-44i−4i4i−4i4-4-44-444i−4i00−4i4i00−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i-44-444-4−4i4i00−4i4i004i−4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-4−4i4i−4i4i4-4-44-44−4i4i004i−4i004i−4i00000000000000000000000000000000000000000000000000000000000000
χ7644-4-4−4i4i−4i4i-44-444-44i−4i004i−4i00−4i4i00000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i−4i4i000000004i−4i004-400000000000000002+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ784-44-44i−4i−4i4i000000004i−4i004-40000000000000000−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ794-44-44i−4i−4i4i00000000−4i4i00-4400000000000000002−2i−2+2i−2−2i2+2i−2+2i2−2i2+2i−2−2i0000000000000000000000000000000000000000
χ804-44-44i−4i−4i4i00000000−4i4i00-440000000000000000−2+2i2−2i2+2i−2−2i2−2i−2+2i−2−2i2+2i0000000000000000000000000000000000000000
χ814-44-4−4i4i4i−4i000000004i−4i00-4400000000000000002+2i−2−2i−2+2i2−2i−2−2i2+2i2−2i−2+2i0000000000000000000000000000000000000000
χ824-44-4−4i4i4i−4i000000004i−4i00-440000000000000000−2−2i2+2i2−2i−2+2i2+2i−2−2i−2+2i2−2i0000000000000000000000000000000000000000
χ834-44-4−4i4i4i−4i00000000−4i4i004-400000000000000002−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ844-44-4−4i4i4i−4i00000000−4i4i004-40000000000000000−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ858-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).