Finite Group Databasebeta

← Group #110618

Character table — Group #110618

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12224444222244444444444424444444444444444444448888888888888888888888888888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-11111-1-1−i−iii
χ1211111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1-1-111ii−i−i
χ1311111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1-1-111−i−iii
χ1611111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i
χ171111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1i−ii−i1-11-1
χ181111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11−ii−ii-11-11
χ191111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11i−ii−i-11-11
χ201111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1−ii−ii1-11-1
χ211111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11−ii−ii1-11-1
χ221111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1i−ii−i-11-11
χ231111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1−ii−ii-11-11
χ241111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11i−ii−i1-11-1
χ251111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1−iii−i−iii−i
χ261111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11i−i−iii−i−ii
χ271111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11−iii−ii−i−ii
χ281111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1i−i−ii−iii−i
χ291111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11i−i−ii−iii−i
χ301111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1−iii−ii−i−ii
χ311111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1i−i−iii−i−ii
χ321111-1-1-1-1-1-111-1-111111-1-1-1-11-111-1-11−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11−iii−i−iii−i
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χ34222222222222222-2-2-2-2-2-2-2-2222-2-2-2-200000000000000000000000000000000-2-222-2-222-2-222-2-22200000000000000000000
χ352222222222-2-2-2-2222-2-222-2-22-2-2-2-222000000000000000022-2-222-2-222-2-222-2-2000000000000000000000000000000000000
χ362222222222-2-2-2-2222-2-222-2-22-2-2-2-2220000000000000000-2-222-2-222-2-222-2-222000000000000000000000000000000000000
χ372222222222-2-2-2-22-2-222-2-2222-2-222-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ382222222222-2-2-2-22-2-222-2-2222-2-222-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ3922222222-2-22222-222222222-2-2-2-2-2-2-2000000000000000022-2-222-2-2-2-222-2-222000000000000000000000000000000000000
χ4022222222-2-22222-222222222-2-2-2-2-2-2-20000000000000000-2-222-2-22222-2-222-2-2000000000000000000000000000000000000
χ4122222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ4222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-222-2-222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-222-2-22200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000
χ452222-2-2-2-22222-2-2-22222-2-2-2-2-22-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ462222-2-2-2-22222-2-2-22222-2-2-2-2-22-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-2-22222-22-22-2-2222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-2-22222-22-22-2-22-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ492222-2-2-2-222-2-222-2-2-22222-2-2-2-22-22-22000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ502222-2-2-2-222-2-222-2-2-22222-2-2-2-22-22-2200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ512222-2-2-2-2-2-222-2-22-2-2-2-222222-22-222-20000000000000000000000000000000022-2-2-2-222-2-22222-2-200000000000000000000
χ522222-2-2-2-2-2-222-2-22-2-2-2-222222-22-222-200000000000000000000000000000000-2-22222-2-222-2-2-2-22200000000000000000000
χ532222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222-2-22222-2-222-22-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222-2-22222-2-222-22-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ572-22-22i2i−2i−2i002-22i−2i02-22-22i−2i2i−2i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ3002ζ−2ζ2ζ−2ζ002ζ3−2ζ3002−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000000000000000
χ582-22-22i2i−2i−2i002-22i−2i02-22-22i−2i2i−2i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ300−2ζ2ζ−2ζ2ζ00−2ζ32ζ300−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000000000000000
χ592-22-22i2i−2i−2i002-22i−2i02-22-22i−2i2i−2i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ3002ζ−2ζ2ζ−2ζ002ζ3−2ζ300−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000000000000000
χ602-22-22i2i−2i−2i002-22i−2i02-22-22i−2i2i−2i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ300−2ζ2ζ−2ζ2ζ00−2ζ32ζ3002−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000000000000000
χ612-22-22i2i−2i−2i002-22i−2i0-22-22−2i2i−2i2i00000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ−2ζ002ζ3−2ζ300002ζ3−2ζ3002ζ−2ζ2−2−22i2−i2−i2i2i2−i2−i2i22−2−2200000000000000000000
χ622-22-22i2i−2i−2i002-22i−2i0-22-22−2i2i−2i2i00000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ2ζ00−2ζ32ζ30000−2ζ32ζ300−2ζ2ζ−222−2−i2i2i2−i2−i2i2i2−i2−222−200000000000000000000
χ632-22-22i2i−2i−2i002-22i−2i0-22-22−2i2i−2i2i0000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ−2ζ002ζ3−2ζ300002ζ3−2ζ3002ζ−2ζ−222−2−i2i2i2−i2−i2i2i2−i2−222−200000000000000000000
χ642-22-22i2i−2i−2i002-22i−2i0-22-22−2i2i−2i2i0000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ2ζ00−2ζ32ζ30000−2ζ32ζ300−2ζ2ζ2−2−22i2−i2−i2i2i2−i2−i2i22−2−2200000000000000000000
χ652-22-22i2i−2i−2i00-22−2i2i02-2-222i−2i−2i2i00000001−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ−2ζ2ζ00−2ζ32ζ300−i2i2−i2i22−22−2−22−22i2−i2i2−i200000000000000000000
χ662-22-22i2i−2i−2i00-22−2i2i02-2-222i−2i−2i2i00000001−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ2ζ−2ζ002ζ3−2ζ300i2−i2i2−i2−22−222−22−2−i2i2−i2i200000000000000000000
χ672-22-22i2i−2i−2i00-22−2i2i02-2-222i−2i−2i2i0000000−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ−2ζ2ζ00−2ζ32ζ300i2−i2i2−i2−22−222−22−2−i2i2−i2i200000000000000000000
χ682-22-22i2i−2i−2i00-22−2i2i02-2-222i−2i−2i2i0000000−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ2ζ−2ζ002ζ3−2ζ300−i2i2−i2i22−22−2−22−22i2−i2i2−i200000000000000000000
χ692-22-22i2i−2i−2i00-22−2i2i0-222-2−2i2i2i−2i00000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ30000−2ζ32ζ300−2ζ2ζi2−i2−i2i2−222−22−2−22−i2i2i2−i200000000000000000000
χ702-22-22i2i−2i−2i00-22−2i2i0-222-2−2i2i2i−2i00000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300002ζ3−2ζ3002ζ−2ζ−i2i2i2−i22−2−22−222−2i2−i2−i2i200000000000000000000
χ712-22-22i2i−2i−2i00-22−2i2i0-222-2−2i2i2i−2i0000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ30000−2ζ32ζ300−2ζ2ζ−i2i2i2−i22−2−22−222−2i2−i2−i2i200000000000000000000
χ722-22-22i2i−2i−2i00-22−2i2i0-222-2−2i2i2i−2i0000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300002ζ3−2ζ3002ζ−2ζi2−i2−i2i2−222−22−2−22−i2i2i2−i200000000000000000000
χ732-22-2−2i−2i2i2i002-2−2i2i02-22-2−2i2i−2i2i00000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ002ζ3−2ζ32ζ3−2ζ3002ζ−2ζ00−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000000000000000
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χ8944-4-44-44-44-40000400000000-40000000000000000000000000000000000000000000000000000002-22-22-22-2000000000000
χ9044-4-44-44-44-40000400000000-4000000000000000000000000000000000000000000000000000000-22-22-22-22000000000000
χ9144-4-44-44-4-440000-40000000040000000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ9244-4-44-44-4-440000-4000000004000000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ9344-4-4-44-444-40000-40000000040000000000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ9444-4-4-44-444-40000-4000000004000000000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ9544-4-4-44-44-440000400000000-40000000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ9644-4-4-44-44-440000400000000-4000000000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ978-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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