Finite Group Databasebeta

← Group #213337

Character table — Group #213337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444224444444444888888888888888888888888444444448888888888888888888888888888888888882224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-1-1-11111-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-11-11-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-111-11-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ171111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1i−ii−ii−ii−i
χ181111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−ii−ii−ii−ii
χ191111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiii−ii−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii11-1-11-1-11−iii−ii−i−ii
χ201111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiii−ii−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii-1-111-111-1i−i−ii−iii−i
χ211111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−ii−ii−i-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-11-11-11-1i−ii−i−ii−ii
χ221111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−ii−ii−i-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-11-11-11−ii−iii−ii−i
χ231111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiii−ii−i-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i1-1-11-1-111−iii−i−iii−i
χ241111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiii−ii−i-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-111-111-1-1i−i−iii−i−ii
χ251111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−ii−ii-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii1-1-11-1-111i−i−iii−i−ii
χ261111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−ii−ii-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-111-111-1-1−iii−i−iii−i
χ271111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−ii−ii-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-11-11-11-1−ii−iii−ii−i
χ281111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−ii−ii-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-11-11-11i−ii−i−ii−ii
χ291111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−ii−ii1111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i11-1-11-1-11i−i−ii−iii−i
χ301111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−ii−ii1111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i-1-111-111-1−iii−ii−i−ii
χ311111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−ii−ii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−ii−ii−ii−ii
χ321111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−ii−ii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111i−ii−ii−ii−i
χ332222222222-2-2-2-2-2-2-2-2222222-2-2-2-2000000000000000022-2-222-2-222-2-20000000022-2-222-2-200000000000000000000000000000000
χ342222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000-2-222-2-22222-2-200000000-2-222-2-22200000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000022-2-222-2-2-2-22200000000-2-222-2-22200000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000-2-222-2-222-2-2220000000022-2-222-2-200000000000000000000000000000000
χ3722222222-2-222-2-222-2-2-2-2222222222222-2-2-2-22222-2-2-2-200000000-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ3822222222-2-222-2-222-2-2-2-222222222-2-2-2-22222-2-2-2-2222200000000-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000002222-2-222-2-2220000000000000000000000000000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000222222-2-222-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-222-2-22222-2-2-2-2000000000000000000000000-2-222000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ4222222222-2-2-2-222-2-222-2-22222-2-2-2-2000000000000000000000000-2-2220000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ4322222222-2-2-2-222-2-222-2-2-2-2-2-2222200000000000000000000000022-2-2000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4422222222-2-2-2-222-2-222-2-2-2-2-2-2222200000000000000000000000022-2-20000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ452222-2-2-2-22222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000−2i2i−2i2i22-2-2-2-2220000000000000000000000000000000000000000
χ462222-2-2-2-22222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000−2i2i−2i2i-2-22222-2-20000000000000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000002i−2i2i−2i-2-22222-2-20000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000002i−2i2i−2i22-2-2-2-2220000000000000000000000000000000000000000
χ492222-2-2-2-222-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000
χ502222-2-2-2-222-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i0000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000
χ512222-2-2-2-222-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000
χ522222-2-2-2-222-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i0000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000
χ532222-2-2-2-2-2-2-2-2-2-22222222i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i0000000022-2-2-2-22200000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-2-2-22222222i2i−2i−2i−2i−2i2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i00000000-2-22222-2-200000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2-2-2222222−2i−2i2i2i2i2i−2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i−2i2i2i−2i00000000-2-22222-2-200000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-2222222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i0000000022-2-2-2-22200000000000000000000000000000000
χ5722-2-22i−2i2i−2i002-2002i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i0000002-2002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5822-2-22i−2i2i−2i002-2002i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-2002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5922-2-22i−2i2i−2i002-2002i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i000000-2200−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6022-2-22i−2i2i−2i002-2002i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000-2200−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6122-2-22i−2i2i−2i002-2002i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i000000-2200−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6222-2-22i−2i2i−2i002-2002i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000-2200−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6322-2-22i−2i2i−2i002-2002i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i0000002-2002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6422-2-22i−2i2i−2i002-2002i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-2002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6522-2-22i−2i2i−2i00-2200−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ300001+i−1−i−1−i1+i1−i−1+i−1+i1−i00002-2002i−2i002−2−22i2−i2−i2i22−2−22i2−i2−i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ6622-2-22i−2i2i−2i00-2200−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ30000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00002-2002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ6722-2-22i−2i2i−2i00-2200−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ300001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000-2200−2i2i002−2−22i2−i2−i2i2−222−2−i2i2i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ6822-2-22i−2i2i−2i00-2200−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ30000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000-2200−2i2i00−222−2−i2i2i2−i22−2−22i2−i2−i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ6922-2-22i−2i2i−2i00-2200−2i2i0000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ300001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000-2200−2i2i00−222−2−i2i2i2−i22−2−22i2−i2−i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
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χ7122-2-22i−2i2i−2i00-2200−2i2i0000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ300001+i−1−i−1−i1+i1−i−1+i−1+i1−i00002-2002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
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χ1044-4-44-4-444-44000000004-400000000−222222−22−222222−2222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000

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