Finite Group Databasebeta

← Group #96751

Character table — Group #96751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444448888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1
χ171111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ221111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ231111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241111-1-1-1111-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-11-1-11−iii−i
χ261111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-111-1i−i−ii
χ271111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-111-1i−i−ii
χ281111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1-11−iii−i
χ291111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1-11i−i−ii
χ301111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-111-1−iii−i
χ311111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-111-1−iii−i
χ321111-1-1-1111-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-11-1-11i−i−ii
χ33222222222222222222-2-222-2-222-2-222-2-2-2-2-2-222-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000
χ352222222222222222-2-222-2-222-2-222-2-222-2-2-2-222-2-222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ362222222222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ372222-2-2-2222-2-2-22-2-222-2-2-2-22222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ382222-2-2-2222-2-2-22-2-222-2-2-2-22222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ392222-2-2-2222-2-2-22-2-2-2-22222-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ402222-2-2-2222-2-2-22-2-2-2-22222-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ41222-222-22-2-22-2-2-2-22002i−2i002i−2i002i−2i002i−2i0000002-2002-22i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ42222-222-22-2-22-2-2-2-22002i−2i002i−2i002i−2i002i−2i0000002-2002-22i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ43222-222-22-2-22-2-2-2-22002i−2i002i−2i002i−2i002i−2i000000-2200-22−2i2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ44222-222-22-2-22-2-2-2-22002i−2i002i−2i002i−2i002i−2i000000-2200-22−2i2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ45222-222-22-2-22-2-2-2-2200−2i2i00−2i2i00−2i2i00−2i2i0000002-2002-2−2i2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ46222-222-22-2-22-2-2-2-2200−2i2i00−2i2i00−2i2i00−2i2i0000002-2002-2−2i2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ47222-222-22-2-22-2-2-2-2200−2i2i00−2i2i00−2i2i00−2i2i000000-2200-222i−2i2i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ48222-222-22-2-22-2-2-2-2200−2i2i00−2i2i00−2i2i00−2i2i000000-2200-222i−2i2i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ49222-2-2-222-2-2-222-22-2002i−2i00−2i2i002i−2i00−2i2i0000002i−2i00−2i2i-222-200001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ50222-2-2-222-2-2-222-22-2002i−2i00−2i2i002i−2i00−2i2i0000002i−2i00−2i2i-222-20000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ51222-2-2-222-2-2-222-22-2002i−2i00−2i2i002i−2i00−2i2i000000−2i2i002i−2i2-2-2200001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ52222-2-2-222-2-2-222-22-2002i−2i00−2i2i002i−2i00−2i2i000000−2i2i002i−2i2-2-220000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ53222-2-2-222-2-2-222-22-200−2i2i002i−2i00−2i2i002i−2i0000002i−2i00−2i2i2-2-2200001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ54222-2-2-222-2-2-222-22-200−2i2i002i−2i00−2i2i002i−2i0000002i−2i00−2i2i2-2-220000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ55222-2-2-222-2-2-222-22-200−2i2i002i−2i00−2i2i002i−2i000000−2i2i002i−2i-222-200001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ56222-2-2-222-2-2-222-22-200−2i2i002i−2i00−2i2i002i−2i000000−2i2i002i−2i-222-20000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ5722-222-22-22-2-22-2-2-222i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2-22-200000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000
χ5822-222-22-22-2-22-2-2-222i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000
χ5922-222-22-22-2-22-2-2-222i−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i-22-22000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ6022-222-22-22-2-22-2-2-222i−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i-22-2200000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ6122-222-22-22-2-22-2-2-22−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i-22-22000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ6222-222-22-22-2-22-2-2-22−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i-22-2200000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ6322-222-22-22-2-22-2-2-22−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i2-22-200000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000
χ6422-222-22-22-2-22-2-2-22−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000
χ6522-22-22-2-22-22-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i2-2-2200000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000
χ6622-22-22-2-22-22-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i2-2-220000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000
χ6722-22-22-2-22-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i-222-2000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ6822-22-22-2-22-22-22-22-22i−2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i-222-200000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ6922-22-22-2-22-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i−2i2i-222-2000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ7022-22-22-2-22-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i−2i2i-222-200000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ7122-22-22-2-22-22-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2-2-2200000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000
χ7222-22-22-2-22-22-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i2-2-220000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000
χ7344-4-44-4-4-4-44-4-44444004400-4-400-4-40044000000000000000000000000000000000000000000000000000000000000
χ7444-4-44-4-4-4-44-4-4444400-4-40044004400-4-4000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-4444-44-4-40044004400-4-400-4-4000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-4444-44-4-400-4-400-4-400440044000000000000000000000000000000000000000000000000000000000000
χ774-4444-4-4-4-4444-4-44-44i−4i004i−4i00−4i4i00−4i4i00000000000000000000000000000000000000000000000000000000000000
χ784-4444-4-4-4-4444-4-44-4−4i4i00−4i4i004i−4i004i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-444-444-4-44-4-44-4-444i−4i00−4i4i00−4i4i004i−4i00000000000000000000000000000000000000000000000000000000000000
χ804-444-444-4-44-4-44-4-44−4i4i004i−4i004i−4i00−4i4i00000000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-44-44-444-4-4000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ824-44-44-44-44-44-444-4-400000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ834-44-4-44-4-44-4-44-4444000000000000000000000000000000004-4-440000000000000000000000000000000000000000
χ844-44-4-44-4-44-4-44-444400000000000000000000000000000000-444-40000000000000000000000000000000000000000
χ854-4-4444-44-4-4-4444-4-444004400-4-400-4-400000000000000000000000000000000000000000000000000000000000000
χ864-4-4444-44-4-4-4444-4-4-4-400-4-40044004400000000000000000000000000000000000000000000000000000000000000
χ874-4-44-4-444-4-44-4-44444400-4-400-4-4004400000000000000000000000000000000000000000000000000000000000000
χ884-4-44-4-444-4-44-4-4444-4-40044004400-4-400000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4444444-4-4-4-44-4000000000000000000004i−4i004i−4i00000000000000000000000000000000000000000000000000
χ904-4-4-4444444-4-4-4-44-400000000000000000000−4i4i00−4i4i00000000000000000000000000000000000000000000000000
χ914-4-4-4-4-4-4444444-4-44000000000000000000004-400-4400000000000000000000000000000000000000000000000000
χ924-4-4-4-4-4-4444444-4-4400000000000000000000-44004-400000000000000000000000000000000000000000000000000

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