Finite Group Databasebeta

← Group #481396

Character table — Group #481396

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11111111222222222222222222222222222222222222222244444444444444444444444444444444444444444488888888161616161616161616161616
order122244442244444444444444888888881616161616161616161616161616161622444488888888888816161616161616161616161616161616161616161616161622448888244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ511111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ611111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-11111
χ811111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1111111-1-1-1-1
χ911111111-1-111-1-11111-1-1-1-1111111111111111111111111111-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1
χ1011111111-1-111-1-11111-1-1-1-1111111111111111111111111111-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ1111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-111-1-1-1-1-1-1111111111111111111111111111111-11-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ1411111111-1-111-1-1-1-1-1-1111111111111111111111111111111-11-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ171111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1-11-11-1i−ii−ii−i
χ181111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-11-11-11−ii−ii−ii
χ191111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1-11-11-1−ii−ii−ii
χ201111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-11-11-11i−ii−ii−i
χ211111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-11-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i1-1-11-11i−i−ii−ii
χ221111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-11-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii-111-11-1−iii−ii−i
χ231111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-11-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii1-1-11-11−iii−ii−i
χ241111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-11-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−i-111-11-1i−i−ii−ii
χ251111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-11-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-111-1-11−iii−i−ii
χ261111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-11-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii1-1-111-1i−i−iii−i
χ271111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-11-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-111-1-11i−i−iii−i
χ281111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-11-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i1-1-111-1−iii−i−ii
χ291111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i-11-111-1−ii−iii−i
χ301111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii1-11-1-11i−ii−i−ii
χ311111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iii-11-111-1i−ii−i−ii
χ321111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i1-11-1-11−ii−iii−i
χ33222222222222222222222222-2-2-2-2-2-2-2-20000000000000000222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ3422222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-222-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ352222222222-2-22222222222-2-2000000002222−2−2−2−22222−2−2−2−2-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−222−2−222−2−200000000000000000000
χ362222222222-2-22222222222-2-200000000−2−2−2−22222−2−2−2−22222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−222−2−222−2−22200000000000000000000
χ372222222222-2-222-2-2-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−222-2-22200000000000022−2−222−2−2−2−222−2−222−2−222−2−22200000000000000000000
χ382222222222-2-222-2-2-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−2222222-2-222000000000000−2−222−2−22222−2−222−2−222−2−222−2−200000000000000000000
χ3922222222-2-222-2-22222-2-2-2-222-2-2-2-2-2-2-2-200000000000000002-2-2-22-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ4022222222-2-222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000-22-2-2-2222222222-2-2-2-200000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-2222-22000000000000−2−222−2−22222−2−222−2−2−2−222−2−22200000000000000000000
χ4222222222-2-2-2-2-2-22222-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−22222-2222-2200000000000022−2−222−2−2−2−222−2−22222−2−222−2−200000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−22-2222-2000000000000−2−222−2−222−2−222−2−22222−2−222−2−200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−222222-2222-200000000000022−2−222−2−222−2−222−2−2−2−222−2−22200000000000000000000
χ452222-2-2-2-22222-2-222-2-222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-22-222-2000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ462222-2-2-2-22222-2-222-2-222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-22-222-2000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-22-22000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ482222-2-2-2-22222-2-2-2-222-2-222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-22-22000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ492222-2-2-2-222-2-2-2-222-2-222-2-222-2-2-2-2222200000000000000002-22-2-22-2-222-2-222-2-22200000000000000000000000000000000000000000000
χ502222-2-2-2-222-2-2-2-2-2-222-2-22222-2-2-2-222220000000000000000-222-22-2-2-22222-2-222-2-200000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2222222-2-2-2-222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-22-222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ522222-2-2-2-2-2-2222222-2-2-2-222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-22-222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ532222-2-2-2-2-2-22222-2-22222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2222-2-2-2000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ542222-2-2-2-2-2-22222-2-22222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2222-2-2-2000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000022-22-2-222-2-2-2-22222-2-200000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-222220000000000000000-2-2-222222-2-222-2-2-2-22200000000000000000000000000000000000000000000
χ5722-2-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i0022−2−222−2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50000002−22−2i2−i2i2−i2i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000000000000000
χ5822-2-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i0022−2−222−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−22−2i2−i2i2−i2i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ700000000000000000000
χ5922-2-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00−2−222−2−222ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−22−22−i2i2−i2i2−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ500000000000000000000
χ6022-2-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00−2−222−2−222−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−22−22−i2i2−i2i2−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ500000000000000000000
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χ6222-2-222-2-22-2002-2−2i2i−2i2i−2i2i−2i2i0022−2−222−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−22−2−i2i2−i2i2−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000000000000000
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χ1104-4-44−4i4i4i−4i0000000000000000−222222−222i2−2i2−2i22i2−2ζ−2ζ32ζ+2ζ32ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ+2ζ32ζ−2ζ300000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.