Finite Group Databasebeta

← Group #96331

Character table — Group #96331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444444444444444444444444444422444444444488888888888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−ii−iii−ii−i
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−ii−ii−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-11111-1-1i−i−iii−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-11111-1-1−iii−i−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-11111-1-1−iii−ii−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-111-1-1-1-111i−i−ii−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-11111-1-1i−i−ii−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-111-1-1-1-111−iii−ii−i−ii
χ3322222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222222222-2-2-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222222222-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ412222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000000002ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ422222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ432222-2-2-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i-22-22000000002ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ0000000000000000000000000000000000000000
χ442222-2-2-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i-22-2200000000−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ452222-2-2-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i-22-22000000002ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
χ462222-2-2-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i-22-2200000000−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ30000000000000000000000000000000000000000
χ472222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ482222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ492222-2-2-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000−2i−2i2i2i−2i−2i2i2i2-2-22000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ502222-2-2-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000−2i−2i2i2i−2i−2i2i2i2-2-2200000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ0000000000000000000000000000000000000000
χ512222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i−2i−2i2i2i-222-20000000000000000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ522222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i−2i−2i2i2i-222-2000000000000000000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ532222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i-222-20000000000000000000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ542222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i-222-2000000000000000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ552222-2-2-2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i00000000000000002i2i−2i−2i2i2i−2i−2i2-2-22000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ30000000000000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i00000000000000002i2i−2i−2i2i2i−2i−2i2-2-2200000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
χ5722-2-222-2-22i−2i2i−2i2i−2i2i−2i00002-22-222-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000i2−i22−22−2i2−i2i2−i22−22−2i2−i200000000
χ5822-2-222-2-22i−2i2i−2i2i−2i2i−2i00002-22-222-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000−i2i2−22−22−i2i2−i2i2−22−22−i2i200000000
χ5922-2-222-2-22i−2i2i−2i2i−2i2i−2i00002-22-2-2-222−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i000000000000000000000000000000000000000000000000i2−i22−22−2i2−i2−i2i2−22−22−i2i200000000
χ6022-2-222-2-22i−2i2i−2i2i−2i2i−2i00002-22-2-2-222−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i000000000000000000000000000000000000000000000000−i2i2−22−22−i2i2i2−i22−22−2i2−i200000000
χ6122-2-222-2-22i−2i2i−2i2i−2i2i−2i0000-22-2222-2-22i2i−2i−2i−2i−2i2i2i-2-222−2i2i−2i2i0000000000000000000000000000000000000000000000002−2−i2i2i2−i2−222−2−i2i2i2−i2−2200000000
χ6222-2-222-2-22i−2i2i−2i2i−2i2i−2i0000-22-2222-2-22i2i−2i−2i−2i−2i2i2i-2-222−2i2i−2i2i000000000000000000000000000000000000000000000000−22i2−i2−i2i22−2−22i2−i2−i2i22−200000000
χ6322-2-222-2-22i−2i2i−2i2i−2i2i−2i0000-22-22-2-222−2i−2i2i2i2i2i−2i−2i22-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000002−2−i2i2i2−i2−22−22i2−i2−i2i22−200000000
χ6422-2-222-2-22i−2i2i−2i2i−2i2i−2i0000-22-22-2-222−2i−2i2i2i2i2i−2i−2i22-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000−22i2−i2−i2i22−22−2−i2i2i2−i2−2200000000
χ6522-2-222-2-2−2i2i−2i2i−2i2i−2i2i00002-22-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000i2−i2−22−22i2−i2i2−i2−22−22i2−i200000000
χ6622-2-222-2-2−2i2i−2i2i−2i2i−2i2i00002-22-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000−i2i22−22−2−i2i2−i2i22−22−2−i2i200000000
χ6722-2-222-2-2−2i2i−2i2i−2i2i−2i2i00002-22-2-2-2222i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i000000000000000000000000000000000000000000000000i2−i2−22−22i2−i2−i2i22−22−2−i2i200000000
χ6822-2-222-2-2−2i2i−2i2i−2i2i−2i2i00002-22-2-2-2222i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i000000000000000000000000000000000000000000000000−i2i22−22−2−i2i2i2−i2−22−22i2−i200000000
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χ1144-4-44-444-444-4-4-4-44400000000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44-444-4-4-44444-4-4000000004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-444-4-4-44444-4-400000000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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