Finite Group Databasebeta

← Group #206418

Character table — Group #206418

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222244444444444444444444444444444444244444444444888888888888888888888888888888882444444488888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-11111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-11111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1211111111-1-11111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1311111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1411111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1511111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ171111-1-1-1-111-1-111-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-111-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ181111-1-1-1-111-1-111-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-111-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ191111-1-1-1-111-1-111-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-111-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ201111-1-1-1-111-1-111-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-111-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ211111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-111-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ221111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-111-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ231111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-111-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ241111-1-1-1-111-1-111-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-111-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-1-1-1111111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11i−i−iii−i−ii
χ261111-1-1-1-1-1-1-1-1111111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−iii−i−iii−i
χ271111-1-1-1-1-1-1-1-1111111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1i−i−ii−iii−i
χ281111-1-1-1-1-1-1-1-1111111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11−iii−ii−i−ii
χ291111-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−iii−i−iii−i
χ301111-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−i−iii−i−ii
χ311111-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11iiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−iii−ii−i−ii
χ321111-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11iiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-11-1-11i−i−ii−iii−i
χ332222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222-2-2-2-22222-2-222220000000000000000-2-222-2-2-2-200000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ362222222222-2-2-2-22222-2-222220000000000000000-2-222-2-2-2-2000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ372222222222-2-2-2-222-2-222-2-2-2-2000000000000000022-2-2-2-2220000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222-2-2-2-222-2-222-2-2-2-2000000000000000022-2-2-2-22200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-222222200000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-2222222000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2222222000000000000000022-2-222-2-20000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2222222000000000000000022-2-222-2-200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-2222222-2-20000000000000000-2-2-2-22-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ462222-2-2-2-22222-2-2-2-2222222-2-20000000000000000-2-2-2-22-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222000000000000000022222-22-20000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222000000000000000022222-22-200000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ492222-2-2-2-222-2-222-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-222-22-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ502222-2-2-2-222-2-222-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-222-22-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-222-2-2222222-2-2220000000000000000-2-2-2-2-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ522222-2-2-2-2-2-222-2-2222222-2-2220000000000000000-2-2-2-2-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ532222-2-2-2-2-2-222-2-222-2-2-2-222-2-200000000000000002222-22-220000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ542222-2-2-2-2-2-222-2-222-2-2-2-222-2-200000000000000002222-22-2200000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2222-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2222-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ572-22-22i−2i2i−2i2-200002i−2i2-2002-22i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i22−22−2i2−i2i2−i22−22−2002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ0000000000000000
χ582-22-22i−2i2i−2i2-200002i−2i2-2002-22i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2−22−22−i2i2−i2i2−22−2200−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ592-22-22i−2i2i−2i2-200002i−2i2-2002-22i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i22−22−2i2−i2i2−i22−22−200−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ602-22-22i−2i2i−2i2-200002i−2i2-2002-22i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2−22−22−i2i2−i2i2−22−22002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ0000000000000000
χ612-22-22i−2i2i−2i2-200002i−2i-2200-22−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−ii2−i2−i2i22−2−22i2−i2−i2i22−2−222ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ000000000000000000
χ622-22-22i−2i2i−2i2-200002i−2i-2200-22−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i−i2i2i2−i2−222−2−i2i2i2−i2−222−2−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ000000000000000000
χ632-22-22i−2i2i−2i2-200002i−2i-2200-22−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−i2i22−2−22i2−i2−i2i22−2−22−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ000000000000000000
χ642-22-22i−2i2i−2i2-200002i−2i-2200-22−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−i2i2i2−i2−222−2−i2i2i2−i2−222−22ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ000000000000000000
χ652-22-22i−2i2i−2i-220000−2i2i2-200-22−2i2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i22−22−2−i2i2−i2i2−22−22002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ662-22-22i−2i2i−2i-220000−2i2i2-200-22−2i2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2−22−22i2−i2i2−i22−22−200−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3002ζ−2ζ0000000000000000
χ672-22-22i−2i2i−2i-220000−2i2i2-200-22−2i2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i22−22−2−i2i2−i2i2−22−2200−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3002ζ−2ζ0000000000000000
χ682-22-22i−2i2i−2i-220000−2i2i2-200-22−2i2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2−22−22i2−i2i2−i22−22−2002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ300−2ζ2ζ0000000000000000
χ692-22-22i−2i2i−2i-220000−2i2i-22002-22i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−i2i22−2−22−i2i2i2−i2−222−22ζ3−2ζ3002ζ−2ζ00−2ζ32ζ300−2ζ2ζ000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.