Finite Group Databasebeta

← Group #134304

Character table — Group #134304

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122244442222224444444444444444444444888888884444444444444444888888888888888888888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ121111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ131111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ζ−ζζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ181111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−ζζ−ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ191111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ζ−ζζ3−ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ201111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−ζζ−ζ3ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ211111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ζ3−ζ3−ζζζ−ζ−ζ3ζ3ζ3−ζ3−ζζζ−ζ−ζ3ζ3
χ221111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−ζ3ζ3ζ−ζ−ζζζ3−ζ3−ζ3ζ3ζ−ζ−ζζζ3−ζ3
χ231111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ζ3−ζ3−ζζζ−ζ−ζ3ζ3−ζ3ζ3ζ−ζ−ζζζ3−ζ3
χ241111-1-1-1-111-1-1-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−ζ3ζ3ζ−ζ−ζζζ3−ζ3ζ3−ζ3−ζζζ−ζ−ζ3ζ3
χ251111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ζ−ζ−ζ3ζ3ζ3−ζ3−ζζζ−ζ−ζ3ζ3ζ3−ζ3−ζζ
χ261111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ζζζ3−ζ3−ζ3ζ3ζ−ζ−ζζζ3−ζ3−ζ3ζ3ζ−ζ
χ271111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ζ−ζ−ζ3ζ3ζ3−ζ3−ζζ−ζζζ3−ζ3−ζ3ζ3ζ−ζ
χ281111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−ζζζ3−ζ3−ζ3ζ3ζ−ζζ−ζ−ζ3ζ3ζ3−ζ3−ζζ
χ291111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ζ3−ζ3ζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ301111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ζ3ζ3−ζζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ311111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ζ3−ζ3ζ−ζζ−ζζ3−ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ321111-1-1-1-111-1-1-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−ζ3ζ3−ζζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ332222222222-2-2-2-2-2-2-2220000000000000000-22222222222-2-222-2-200000000-2-2-2-222-2-222-2-200000000000000000000000000000000
χ342222222222-2-2-2-2-2-2-2220000000000000000-222222222-2-222-2-22200000000-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-222-2-222-2-2000000002222-2-222-2-22200000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-2-2-222-2-22200000000222222-2-222-2-200000000000000000000000000000000
χ3722222222-2-222-2-222-2-2-20000000000000000-222-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-222-2-222-2-2-20000000000000000-222-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-222-2-222-2-2-20000000000000000-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i-22-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4022222222-2-222-2-222-2-2-20000000000000000-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i-22-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ4122222222-2-2-2-222-2-22-2-22222-2-2-2-22222-2-2-2-2222-2-222-2-20000000000000000-22-220000000022-2-222-2-2000000000000000000000000
χ4222222222-2-2-2-222-2-22-2-22222-2-2-2-22222-2-2-2-22-2-222-2-22200000000000000002-22-200000000-2-222-2-222000000000000000000000000
χ4322222222-2-2-2-222-2-22-2-2-2-2-2-22222-2-2-2-22222222-2-222-2-20000000000000000-22-2200000000-2-222-2-222000000000000000000000000
χ4422222222-2-2-2-222-2-22-2-2-2-2-2-22222-2-2-2-222222-2-222-2-22200000000000000002-22-20000000022-2-222-2-2000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-2-20000000000000000-22i2i2i2i−2i−2i−2i−2i22-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-20000000000000000-22i2i2i2i−2i−2i−2i−2i-2-22222-2-200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-2222222-2-2-2-2-20000000000000000-2−2i−2i−2i−2i2i2i2i2i22-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ482222-2-2-2-2222222-2-2-2-2-20000000000000000-2−2i−2i−2i−2i2i2i2i2i-2-22222-2-2000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-222-2-2-2-22222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i0000000022-2-2-2-222000000000000000000000000
χ502222-2-2-2-2-2-222-2-2-2-22222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000-2-22222-2-2000000000000000000000000
χ512222-2-2-2-2-2-222-2-2-2-2222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000-2-22222-2-2000000000000000000000000
χ522222-2-2-2-2-2-222-2-2-2-2222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i0000000022-2-2-2-222000000000000000000000000
χ532222-2-2-2-2-2-2-2-22222-2220000000000000000-22i2i−2i−2i−2i−2i2i2i0000000022-2-2-2-2222i−2i−2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ542222-2-2-2-2-2-2-2-22222-2220000000000000000-22i2i−2i−2i−2i−2i2i2i00000000-2-22222-2-22i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ552222-2-2-2-2-2-2-2-22222-2220000000000000000-2−2i−2i2i2i2i2i−2i−2i0000000022-2-2-2-222−2i2i2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ562222-2-2-2-2-2-2-2-22222-2220000000000000000-2−2i−2i2i2i2i2i−2i−2i00000000-2-22222-2-2−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ5722-2-22i−2i2i−2i2-200000002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i02ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000002ζ3−2ζ3002ζ−2ζ2−22−2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ5822-2-22i−2i2i−2i2-200000002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i02ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−2ζ32ζ300−2ζ2ζ2−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ5922-2-22i−2i2i−2i2-200000002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−2ζ32ζ300−2ζ2ζ−22−22−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ6022-2-22i−2i2i−2i2-200000002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000002ζ3−2ζ3002ζ−2ζ−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ6122-2-22i−2i2i−2i2-200000002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i02ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000002ζ3−2ζ3002ζ−2ζ−22−22−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ6222-2-22i−2i2i−2i2-200000002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i02ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−2ζ32ζ300−2ζ2ζ−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ6322-2-22i−2i2i−2i2-200000002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−2ζ32ζ300−2ζ2ζ2−22−2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ6422-2-22i−2i2i−2i2-200000002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000002ζ3−2ζ3002ζ−2ζ2−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ6522-2-22i−2i2i−2i-220000000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i02ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i00002ζ−2ζ002ζ3−2ζ3002−2−22i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ6622-2-22i−2i2i−2i-220000000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i02ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3-2200−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000−2ζ2ζ00−2ζ32ζ3002−2−22i2−i2−i2i22−2−22−i2i2i2−i20000000000000000
χ6722-2-22i−2i2i−2i-220000000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000−2ζ2ζ00−2ζ32ζ300−222−2−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
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χ904-44-444-4-400004-4004000000-44-440000-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ914-44-444-4-40000-4400-4004i−4i4i−4i00004i−4i4i−4i0000400000000000000000000000000000000000000000000000000000000000000000000
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χ934-44-4-4-44400004-400-4004-44-40000-44-440000400000000000000000000000000000000000000000000000000000000000000000000
χ944-44-4-4-44400004-400-400-44-4400004-44-40000400000000000000000000000000000000000000000000000000000000000000000000
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χ1044-4-44−4i4i4i−4i00-44004i−4i000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i2−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000000000000000000000000000

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