Finite Group Databasebeta

← Group #497609

Character table — Group #497609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11111111222222222222222222222222222222222222222244444444444444444444444444444444444444444488888888161616161616161616161616
order122222224444444444444444888888881616161616161616161616161616161644444488888888888816161616161616161616161616161616161616161616161622224444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ511111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1111111-1-1-1-1
χ811111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-11111
χ91111111111-1-1-1-11111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1
χ121111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-111
χ131111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ171-11-1-11-11-1-111-1-111-1-111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−ii−i1-1i−ii−i1-11-1
χ181-11-1-11-11-1-111-1-111-1-111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−ii-11−ii−ii-11-11
χ191-11-1-11-11-1-111-1-111-1-111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−ii1-1−ii−ii1-11-1
χ201-11-1-11-11-1-111-1-111-1-111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−ii−i-11i−ii−i-11-11
χ211-11-1-11-11-1-111-1-1-1-111-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-111-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−ii−i1-1−ii−ii-11-11
χ221-11-1-11-11-1-111-1-1-1-111-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-111-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii−ii-11i−ii−i1-11-1
χ231-11-1-11-11-1-111-1-1-1-111-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-111-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−ii1-1i−ii−i-11-11
χ241-11-1-11-11-1-111-1-1-1-111-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-111-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−ii−i-11−ii−ii1-11-1
χ251-11-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1-11-11-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−ii-11i−i−ii1-1-11
χ261-11-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1-11-11-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiii−i1-1−iii−i-111-1
χ271-11-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1-11-11-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiii−i-11−iii−i1-1-11
χ281-11-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1-11-11-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−ii1-1i−i−ii-111-1
χ291-11-1-11-11-1-1-1-111-1-11111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-1-11-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−ii-11−iii−i-111-1
χ301-11-1-11-11-1-1-1-111-1-11111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-1-11-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiii−i1-1i−i−ii1-1-11
χ311-11-1-11-11-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-1-11-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiii−i-11i−i−ii-111-1
χ321-11-1-11-11-1-1-1-111-1-11111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-1-11-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−ii1-1−iii−i1-1-11
χ33222222222222222222222222-2-2-2-2-2-2-2-20000000000000000222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ3422222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222-2-2-2-22222222200000000000000000000000000000000000000000000
χ352222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ3722222222-2-2222222222222-2-2000000002222−2−2−2−22222−2−2−2−2-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−222−2−222−2−200000000000000000000
χ3822222222-2-2222222222222-2-200000000−2−2−2−22222−2−2−2−22222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−222−2−222−2−22200000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−22222-2-200000000000022−2−222−2−2−2−222−2−222−2−222−2−22200000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−222222222-2-2000000000000−2−222−2−22222−2−222−2−222−2−222−2−200000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-2-22222000000000000−2−222−2−22222−2−222−2−2−2−222−2−22200000000000000000000
χ4222222222-2-2-2-2-2-22222-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−22222-2-2222200000000000022−2−222−2−2−2−222−2−22222−2−222−2−200000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−222-2-222000000000000−2−222−2−222−2−222−2−22222−2−222−2−200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−2222222-2-22200000000000022−2−222−2−222−2−222−2−2−2−222−2−22200000000000000000000
χ452222-2-2-2-22-20000000000002-222-2-222-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000002-22-22-22-2000000000000
χ462222-2-2-2-22-20000000000002-222-2-222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000-22-22-22-22000000000000
χ472222-2-2-2-22-20000000000002-222-2-222-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000002-22-2-22-22000000000000
χ482222-2-2-2-22-20000000000002-222-2-222-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000-22-222-22-2000000000000
χ4922-2-2-222-2002-22-22i−2i2i−2i2i−2i2i−2i002−22−22−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+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
χ5022-2-2-222-2002-22-22i−2i2i−2i2i−2i2i−2i002−22−22−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−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
χ5122-2-2-222-2002-22-22i−2i2i−2i2i−2i2i−2i00−22−22−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−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
χ5222-2-2-222-2002-22-22i−2i2i−2i2i−2i2i−2i00−22−22−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+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
χ5322-2-2-222-2002-22-2−2i2i−2i2i−2i2i−2i2i002−22−22−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000002−22−2−i2i2−i2i2−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−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
χ5422-2-2-222-2002-22-2−2i2i−2i2i−2i2i−2i2i002−22−22−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−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
χ5522-2-2-222-2002-22-2−2i2i−2i2i−2i2i−2i2i00−22−22−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000−22−22i2−i2i2−i2i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+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
χ5622-2-2-222-2002-22-2−2i2i−2i2i−2i2i−2i2i00−22−22−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000−22−22i2−i2i2−i2i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−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
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.