Finite Group Databasebeta

← Group #108572

Character table — Group #108572

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222222222244444444444444444444444444224444444444888888888888888888888888888888884444444488888888
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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ91111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ121111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ131111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i
χ141111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii
χ151111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ161111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ171111-1-1-1-111-1-1-11111-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11-11-11-11-1i−ii−ii−ii−i
χ181111-1-1-1-111-1-1-11111-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-11-11-11-11−ii−ii−ii−ii
χ191111-1-1-1-111-1-1-11111-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1-11-11i−ii−i−ii−ii
χ201111-1-1-1-111-1-1-11111-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-111-11-1−ii−iii−ii−i
χ211111-1-1-1-111-1-1-11111-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1-11-11−ii−iii−ii−i
χ221111-1-1-1-111-1-1-11111-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-111-11-1i−ii−i−ii−ii
χ231111-1-1-1-111-1-1-11111-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11-11-11-11-1−ii−ii−ii−ii
χ241111-1-1-1-111-1-1-11111-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-11-11-11-11i−ii−ii−ii−i
χ251111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii-111-1-111-1
χ261111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i−iii−i1-1-111-1-11
χ271111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii−iii−i-111-11-1-11
χ281111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−ii−i−ii1-1-11-111-1
χ291111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii−iii−i1-1-11-111-1
χ301111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−ii−i−ii-111-11-1-11
χ311111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii1-1-111-1-11
χ321111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i−iii−i-111-1-111-1
χ332222222222-2-2-22222-2-2-2220000000000000000-2-22222-2-2-2-20000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ342222222222-2-2-22222-2-2-2220000000000000000-2-22222-2-2-2-200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-222220000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2222200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ3722222222-2-222-222-2-2-222-2-20000000000000000-2-222-2-22-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-222-222-2-2-222-2-20000000000000000-2-222-2-22-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-222-2-2-222-222-2-20000000000000000-2-2-2-222-22-220000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4022222222-2-222-2-2-222-222-2-20000000000000000-2-2-2-222-22-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4122222222-2-2-2-2222-2-22-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-22-2222-2-222-2-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-2-2222-2-22-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-22-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2222-22-2-2-222-2-222000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-22-2-2222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2222-22-222-2-222-2-2000000000000000000000000000000000000000000000000
χ452222-2-2-2-22222222222-2-2-2-20000000000000000-2-2-2-2-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-22222222222-2-2-2-20000000000000000-2-2-2-2-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-222222-2-2-2-22-2-2-2-20000000000000000-2-22222-2-222000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ482222-2-2-2-222222-2-2-2-22-2-2-2-20000000000000000-2-22222-2-22200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-222-222-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-2-2222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ502222-2-2-2-2-2-222-222-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i22-2-2222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-222-2-2-222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2222-2-2-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ522222-2-2-2-2-2-222-2-2-222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2222-2-2-222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222-2-2222220000000000000000-2-2-2-222-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ542222-2-2-2-2-2-2-2-2222-2-2222220000000000000000-2-2-2-222-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ552222-2-2-2-2-2-2-2-22-2-222222220000000000000000-2-222-2-22-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ562222-2-2-2-2-2-2-2-22-2-222222220000000000000000-2-222-2-22-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ5722-2-22i2i−2i−2i2-20002-22-20002i−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−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζi2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ5822-2-22i2i−2i−2i2-20002-22-20002i−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−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζ−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ5922-2-22i2i−2i−2i2-20002-22-20002i−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−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002ζ−2ζ−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ6022-2-22i2i−2i−2i2-20002-22-20002i−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−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−2ζ2ζi2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ6122-2-22i2i−2i−2i2-2000-22-220002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2i2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ300−2ζ2ζi2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ6222-2-22i2i−2i−2i2-2000-22-220002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2i2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3002ζ−2ζ−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ6322-2-22i2i−2i−2i2-2000-22-220002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2i2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ00−2ζ32ζ300−2ζ2ζ−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ6422-2-22i2i−2i−2i2-2000-22-220002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2i2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ002ζ3−2ζ3002ζ−2ζi2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ6522-2-22i2i−2i−2i-220002-2-22000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i002i−2i−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ−2ζ002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ3002−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ6622-2-22i2i−2i−2i-220002-2-22000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i002i−2i−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ2ζ00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ300−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ6722-2-22i2i−2i−2i-220002-2-22000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i002i−2i−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ−2ζ002ζ3−2ζ3002ζ−2ζ002ζ3−2ζ300−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ6822-2-22i2i−2i−2i-220002-2-22000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i002i−2i−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ2ζ00−2ζ32ζ300−2ζ2ζ00−2ζ32ζ3002−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
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χ7022-2-22i2i−2i−2i-22000-222-2000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00−2i2i2i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ2ζ00−2ζ32ζ3002ζ−2ζ002ζ3−2ζ300−222−2i2−i2−i2i22−2−22−i2i2i2−i20000000000000000
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χ974-4-444-4-44000040000-4000000004i−4i−4i4i0000−4i4i4i−4i4-40000000000000000000000000000000000000000000000000000000000000000
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χ994-4-444-4-440000-40000400004-4-4400004-4-440000-440000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-440000-4000040000-444-40000-444-40000-440000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-4000040000-400004i−4i−4i4i0000−4i4i4i−4i0000-440000000000000000000000000000000000000000000000000000000000000000
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χ1034-4-44-444-40000-400004000000004-4-4400004-4-444-40000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-40000-40000400000000-444-40000-444-44-40000000000000000000000000000000000000000000000000000000000000000

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