Finite Group Databasebeta

← Group #129155

Character table — Group #129155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222244444444444444448888888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ171111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i1-11-11-11-1
χ181111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-11-11-11-11
χ191111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii1-11-1-11-11
χ201111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i-11-111-11-1
χ211111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-11-11-11-11
χ221111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii1-11-11-11-1
χ231111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii-11-111-11-1
χ241111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i1-11-1-11-11
χ251111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iii−i−ii−iii−i−iii−i
χ261111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−iii−ii−i−iii−i−ii
χ271111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−i−iii−ii−i−ii
χ281111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−iii−i−ii−iii−i
χ291111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iii−i−iii−i−iii−i−ii
χ301111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−iii−i−iii−i−iii−i
χ311111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−ii−iii−ii−i−ii−iii−i
χ321111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−ii−i−ii−iii−ii−i−ii
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-200000000000000002-22-22-22-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ362222222222222222-2-2-2-2-2-2-2-200000000000000002-22-22-22-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ372222222222222222-2-2-2-2-2-2-2-20000000000000000-22-22-22-220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ382222222222222222-2-2-2-2-2-2-2-20000000000000000-22-22-22-2200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000002i−2i2i−2i−2i2i−2i2i0000000022−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000002i−2i2i−2i−2i2i−2i2i00000000−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000−2i2i−2i2i2i−2i2i−2i0000000022−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000−2i2i−2i2i2i−2i2i−2i00000000−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ452222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000002i−2i−2i2i2i−2i−2i2i0000000022−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ462222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000002i−2i−2i2i2i−2i−2i2i00000000−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ472222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i0000000022−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ482222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i00000000−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ492222-2-2-2-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ502222-2-2-2-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22222-2-22222-2-2-2-200000000000000002-2-22-222-20000000022−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−20000000000000000
χ522222-2-2-2-2-2-22222-2-22222-2-2-2-200000000000000002-2-22-222-200000000−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−2220000000000000000
χ532222-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000-222-22-2-220000000022−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−2220000000000000000
χ542222-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000-222-22-2-2200000000−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−20000000000000000
χ552222-2-2-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ5722-2-222-2-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζi2−i2i2−i2i2−i2i2−i22−22−22−22−21+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ5822-2-222-2-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−i2i2−i2i2−i2i2−i2i2−22−22−22−22−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ5922-2-222-2-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζi2−i2i2−i2i2−i2i2−i22−22−22−22−2−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ6022-2-222-2-22i−2i2i2i−2i−2i2i−2i2-22i−2i2-22i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−i2i2−i2i2−i2i2−i2i2−22−22−22−221+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ6122-2-222-2-22i−2i2i2i−2i−2i2i−2i-22−2i2i-22−2i2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ30000000000000000
χ6222-2-222-2-22i−2i2i2i−2i−2i2i−2i-22−2i2i-22−2i2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ30000000000000000
χ6322-2-222-2-22i−2i2i2i−2i−2i2i−2i-22−2i2i-22−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i00000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000000000000000000000000000
χ6422-2-222-2-22i−2i2i2i−2i−2i2i−2i-22−2i2i-22−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000000000000000000000000000
χ6522-2-222-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3i2−i2i2−i2i2−i2i2−i2−22−22−22−221−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ6622-2-222-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−i2i2−i2i2−i2i2−i2i22−22−22−22−2−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ6722-2-222-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3i2−i2i2−i2i2−i2i2−i2−22−22−22−22−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ6822-2-222-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−i2i2−i2i2−i2i2−i2i22−22−22−22−21−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ6922-2-222-2-2−2i2i−2i−2i2i2i−2i2i-222i−2i-222i−2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ0000000000000000
χ7022-2-222-2-2−2i2i−2i−2i2i2i−2i2i-222i−2i-222i−2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ0000000000000000
χ7122-2-222-2-2−2i2i−2i−2i2i2i−2i2i-222i−2i-222i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-200000000000000000000000000000000
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χ7322-2-2-2-2222i−2i−2i−2i2i2i2i−2i2-2−2i2i-222i−2i22-2-2−2i−2i2i2i-2-2222i2i−2i−2i00000000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-200000000000000000000000000000000
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χ944-44-4-44-4444-44-44-4-400000000−2222−222222−2222−2222−2222−22−2222−22220000000000000000000000000000000000000000000000000000000000000000
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χ1034-4-44-444-4−4i4i4i−4i−4i4i4i−4i0000000022−22−22222i2−2i2−2i22i2−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4−4i4i4i−4i−4i4i4i−4i00000000−222222−22−2i22i22i2−2i222−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000000000

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