Finite Group Databasebeta

← Group #495461

Character table — Group #495461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order1222222244444444222244444444444488888888888888884444888888881616161616161616161616161616161616161616161616161616161616161616444444444444444444444444
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
χ51111111111111111-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ181111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ191111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ201111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ211111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii
χ221111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i
χ231111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−ii−iii−ii−i
χ241111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−ii−ii−i−ii−ii
χ251111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii
χ261111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i
χ271111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−iii−i−iii−i
χ281111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−ii−i−iii−i−ii
χ291111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ301111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ311111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ321111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ3322222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ3522222222222222222222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ362222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-222-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-2-2220000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−222000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-2-22200000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000022-2-20000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−2000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000022-2-200000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−222000000000000000000000000
χ452222-2-2-2-22222-2-2-2-222-2-222-2-22222-2-2-2-20000000000000000-22-220000000022−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222000000000000000000000000
χ462222-2-2-2-22222-2-2-2-222-2-222-2-22222-2-2-2-20000000000000000-22-2200000000−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2000000000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-22-22-2-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000002-22-20000000022−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−2000000000000000000000000
χ492222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000002-22-200000000−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−222000000000000000000000000
χ502222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-22222-2-2-2-2-22-2222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-222-2-20000000000000000-222-20000000022−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−2000000000000000000000000
χ522222-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-222-2-20000000000000000-222-200000000−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−222000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-22-2-22-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-22222-2-2222222-2-222-2-2-2-200000000000000002-2-220000000022−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−222000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-2222222-2-222-2-2-2-200000000000000002-2-2200000000−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−2000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22222-2-22222222222-2-2-2-2-2-2-2-2-222-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ5722-2-22-22-22i2i−2i−2i2i2i−2i−2i00002-22i−2i2i−2i00002-222-2-22i2i−2i−2i2i2i−2i−2i22-2-200000000000000000000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ5822-2-22-22-22i2i−2i−2i2i2i−2i−2i00002-22i−2i2i−2i00002-222-2-22i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ5922-2-22-22-22i2i−2i−2i2i2i−2i−2i00002-22i−2i2i−2i00002-2-2-222−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ6022-2-22-22-22i2i−2i−2i2i2i−2i−2i00002-22i−2i2i−2i00002-2-2-222−2i−2i2i2i−2i−2i2i2i-2-22200000000000000000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ6122-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002-2−2i2i−2i2i00002-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-200000000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ6222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002-2−2i2i−2i2i00002-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-20000000000000000000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ6322-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002-2−2i2i−2i2i00002-2-2-2222i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ6422-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002-2−2i2i−2i2i00002-2-2-2222i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ6522-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-222i−2i−2i2i00002-222-2-2−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ6622-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-222i−2i−2i2i00002-222-2-2−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ6722-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-222i−2i−2i2i00002-2-2-2222i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ6822-2-2-22-222i2i−2i−2i−2i−2i2i2i0000-222i−2i−2i2i00002-2-2-2222i2i−2i−2i−2i−2i2i2i22-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ6922-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-22−2i2i2i−2i00002-222-2-22i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ7022-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-22−2i2i2i−2i00002-222-2-22i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ7122-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-22−2i2i2i−2i00002-2-2-222−2i−2i2i2i2i2i−2i−2i22-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ7222-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000-22−2i2i2i−2i00002-2-2-222−2i−2i2i2i2i2i−2i−2i22-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
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χ10544-4-44-44-44i4i−4i−4i4i4i−4i−4i0000-44−4i4i−4i4i0000-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10644-4-44-44-4−4i−4i4i4i−4i−4i4i4i0000-444i−4i4i−4i0000-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10744-4-4-44-444i4i−4i−4i−4i−4i4i4i00004-4−4i4i4i−4i0000-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10844-4-4-44-44−4i−4i4i4i4i4i−4i−4i00004-44i−4i−4i4i0000-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1094-4-4444-4-44-4-444-4-44000000000000000022−22−222222−22−222222−22−222222−22−222200000000000000000000000000000000000000000000000000000000000000000000
χ1104-4-4444-4-44-4-444-4-440000000000000000−222222−22−222222−22−222222−22−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1114-4-4444-4-4-444-4-444-4000000000000000022−22−2222−222222−22−222222−2222−22−222200000000000000000000000000000000000000000000000000000000000000000000
χ1124-4-4444-4-4-444-4-444-40000000000000000−222222−2222−22−222222−22−2222−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-4-4444-4-44-444-4000000000000000022−22−2222−222222−2222−22−2222−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-44-4-4444-4-44-444-40000000000000000−222222−2222−22−2222−222222−2222−22−222200000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44-4-444-444-44-4-44000000000000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-4-444-444-44-4-440000000000000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000000000000000000000000000000000000000000000

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