Finite Group Databasebeta

← Group #96874

Character table — Group #96874

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444488888888888888888888888888888888888888888888888822448888
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−i1-11-111-1-1
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-11-11-1-111
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-11-11-1-111
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−iiiii1-11-111-1-1
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−iiiii1-11-1-1-111
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-11-1111-1-1
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-11-1111-1-1
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−i1-11-1-1-111
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-1i−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-1−ii−ii
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111i−ii−i
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111i−ii−i
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-1−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-11-1-11i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-111-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-111-1−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1-11i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-111-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-11-1-11−iii−i
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
χ3722222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ412222-2-2-2-22i2i2i−2i−2i−2i2i−2i002-2002i−2i002-2002i−2i0000002ζ3−2ζ3002ζ−2ζ2ζ3−2ζ32ζ−2ζ0000i2−i22−2i2−i22−21+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ422222-2-2-2-22i2i2i−2i−2i−2i2i−2i002-2002i−2i002-2002i−2i0000002ζ3−2ζ3002ζ−2ζ2ζ3−2ζ32ζ−2ζ0000−i2i2−22−i2i2−22−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ432222-2-2-2-22i2i2i−2i−2i−2i2i−2i002-2002i−2i002-2002i−2i000000−2ζ32ζ300−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000i2−i22−2i2−i22−2−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ442222-2-2-2-22i2i2i−2i−2i−2i2i−2i002-2002i−2i002-2002i−2i000000−2ζ32ζ300−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000−i2i2−22−i2i2−221+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ452222-2-2-2-22i2i2i−2i−2i−2i2i−2i00-2200−2i2i00-2200−2i2i0000002ζ3−2ζ3002ζ−2ζ−2ζ32ζ3−2ζ2ζ00002−2−i2i2−22i2−i21−i−1+i−1−i1+i−1+i1−i1+i−1−i000000000000000000000000
χ462222-2-2-2-22i2i2i−2i−2i−2i2i−2i00-2200−2i2i00-2200−2i2i0000002ζ3−2ζ3002ζ−2ζ−2ζ32ζ3−2ζ2ζ0000−22i2−i22−2−i2i2−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000000000000000000000
χ472222-2-2-2-22i2i2i−2i−2i−2i2i−2i00-2200−2i2i00-2200−2i2i000000−2ζ32ζ300−2ζ2ζ2ζ3−2ζ32ζ−2ζ00002−2−i2i2−22i2−i2−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000000000000000000000
χ482222-2-2-2-22i2i2i−2i−2i−2i2i−2i00-2200−2i2i00-2200−2i2i000000−2ζ32ζ300−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000−22i2−i22−2−i2i21−i−1+i−1−i1+i−1+i1−i1+i−1−i000000000000000000000000
χ492222-2-2-2-2−2i−2i−2i2i2i2i−2i2i002-200−2i2i002-200−2i2i0000002ζ−2ζ002ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000i2−i2−22i2−i2−221−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ502222-2-2-2-2−2i−2i−2i2i2i2i−2i2i002-200−2i2i002-200−2i2i0000002ζ−2ζ002ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000−i2i22−2−i2i22−2−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ512222-2-2-2-2−2i−2i−2i2i2i2i−2i2i002-200−2i2i002-200−2i2i000000−2ζ2ζ00−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000i2−i2−22i2−i2−22−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ522222-2-2-2-2−2i−2i−2i2i2i2i−2i2i002-200−2i2i002-200−2i2i000000−2ζ2ζ00−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000−i2i22−2−i2i22−21−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ532222-2-2-2-2−2i−2i−2i2i2i2i−2i2i00-22002i−2i00-22002i−2i0000002ζ−2ζ002ζ3−2ζ3−2ζ2ζ−2ζ32ζ300002−2i2−i2−22−i2i2−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000000000000000000000
χ542222-2-2-2-2−2i−2i−2i2i2i2i−2i2i00-22002i−2i00-22002i−2i0000002ζ−2ζ002ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000−22−i2i22−2i2−i21+i−1−i−1+i1−i−1−i1+i1−i−1+i000000000000000000000000
χ552222-2-2-2-2−2i−2i−2i2i2i2i−2i2i00-22002i−2i00-22002i−2i000000−2ζ2ζ00−2ζ32ζ32ζ−2ζ2ζ3−2ζ300002−2i2−i2−22−i2i21+i−1−i−1+i1−i−1−i1+i1−i−1+i000000000000000000000000
χ562222-2-2-2-2−2i−2i−2i2i2i2i−2i2i00-22002i−2i00-22002i−2i000000−2ζ2ζ00−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000−22−i2i22−2i2−i2−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000000000000000000000
χ5722-2-222-2-22i2i−2i2i−2i−2i−2i2i2-22-22i−2i2i−2i2-2-222i−2i−2i2i2-22i−2i000000000000000000000000000000002-22i−2i2-22i−2i0000000000000000
χ5822-2-222-2-22i2i−2i2i−2i−2i−2i2i2-22-22i−2i2i−2i2-2-222i−2i−2i2i2-22i−2i00000000000000000000000000000000-22−2i2i-22−2i2i0000000000000000
χ5922-2-222-2-22i2i−2i2i−2i−2i−2i2i2-2-222i−2i−2i2i2-22-22i−2i2i−2i-22−2i2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000
χ6022-2-222-2-22i2i−2i2i−2i−2i−2i2i2-2-222i−2i−2i2i2-22-22i−2i2i−2i-22−2i2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000
χ6122-2-222-2-22i2i−2i2i−2i−2i−2i2i-222-2−2i2i2i−2i-22-22−2i2i−2i2i-22−2i2i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000
χ6222-2-222-2-22i2i−2i2i−2i−2i−2i2i-222-2−2i2i2i−2i-22-22−2i2i−2i2i-22−2i2i0000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000
χ6322-2-222-2-22i2i−2i2i−2i−2i−2i2i-22-22−2i2i−2i2i-222-2−2i2i2i−2i2-22i−2i000000000000000000000000000000002i−2i-22−2i2i2-20000000000000000
χ6422-2-222-2-22i2i−2i2i−2i−2i−2i2i-22-22−2i2i−2i2i-222-2−2i2i2i−2i2-22i−2i00000000000000000000000000000000−2i2i2-22i−2i-220000000000000000
χ6522-2-222-2-2−2i−2i2i−2i2i2i2i−2i2-22-2−2i2i−2i2i2-2-22−2i2i2i−2i2-2−2i2i000000000000000000000000000000002-2−2i2i2-2−2i2i0000000000000000
χ6622-2-222-2-2−2i−2i2i−2i2i2i2i−2i2-22-2−2i2i−2i2i2-2-22−2i2i2i−2i2-2−2i2i00000000000000000000000000000000-222i−2i-222i−2i0000000000000000
χ6722-2-222-2-2−2i−2i2i−2i2i2i2i−2i2-2-22−2i2i2i−2i2-22-2−2i2i−2i2i-222i−2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000
χ6822-2-222-2-2−2i−2i2i−2i2i2i2i−2i2-2-22−2i2i2i−2i2-22-2−2i2i−2i2i-222i−2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000
χ6922-2-222-2-2−2i−2i2i−2i2i2i2i−2i-222-22i−2i−2i2i-22-222i−2i2i−2i-222i−2i00000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000
χ7022-2-222-2-2−2i−2i2i−2i2i2i2i−2i-222-22i−2i−2i2i-22-222i−2i2i−2i-222i−2i0000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000
χ7122-2-222-2-2−2i−2i2i−2i2i2i2i−2i-22-222i−2i2i−2i-222-22i−2i−2i2i2-2−2i2i000000000000000000000000000000002i−2i2-2−2i2i-220000000000000000
χ7222-2-222-2-2−2i−2i2i−2i2i2i2i−2i-22-222i−2i2i−2i-222-22i−2i−2i2i2-2−2i2i00000000000000000000000000000000−2i2i-222i−2i2-20000000000000000
χ7344-4-4-4-44444-4-444-4-40044004400-4-400-4-4000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4-44444-4-444-4-400-4-400-4-400440044000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-4-444-4-444004400-4-400-4-40044000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-4-444-4-44400-4-40044004400-4-4000000000000000000000000000000000000000000000000000000000000
χ774-44-44-44-44i−4i4i−4i4i−4i−4i4i000000000000000000004ζ−4ζ004ζ3−4ζ300000000000000000000000000000000000000000000000000
χ784-44-44-44-44i−4i4i−4i4i−4i−4i4i00000000000000000000−4ζ4ζ00−4ζ34ζ300000000000000000000000000000000000000000000000000
χ794-44-44-44-4−4i4i−4i4i−4i4i4i−4i000000000000000000004ζ3−4ζ3004ζ−4ζ00000000000000000000000000000000000000000000000000
χ804-44-44-44-4−4i4i−4i4i−4i4i4i−4i00000000000000000000−4ζ34ζ300−4ζ4ζ00000000000000000000000000000000000000000000000000
χ814-44-4-44-444-444-44-4-444004400-4-400-4-400000000000000000000000000000000000000000000000000000000000000
χ824-44-4-44-444-444-44-4-4-4-400-4-40044004400000000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-44-44-4-44-4444400-4-400-4-4004400000000000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44-44-4-44-444-4-40044004400-4-400000000000000000000000000000000000000000000000000000000000000
χ854-4-444-4-444-4-4-4-4444000000000000000000000000000000004-44-40000000000000000000000000000000000000000
χ864-4-444-4-444-4-4-4-444400000000000000000000000000000000-44-440000000000000000000000000000000000000000
χ874-4-444-4-44-44444-4-4-4000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ884-4-444-4-44-44444-4-4-400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ894-4-44-444-44i−4i−4i4i4i−4i4i−4i4-4004i−4i00-4400−4i4i00000000000000000000000000000000000000000000000000000000000000
χ904-4-44-444-44i−4i−4i4i4i−4i4i−4i-4400−4i4i004-4004i−4i00000000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-4−4i4i4i−4i−4i4i−4i4i4-400−4i4i00-44004i−4i00000000000000000000000000000000000000000000000000000000000000
χ924-4-44-444-4−4i4i4i−4i−4i4i−4i4i-44004i−4i004-400−4i4i00000000000000000000000000000000000000000000000000000000000000

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