Finite Group Databasebeta

← Group #110271

Character table — Group #110271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444442222444444444444444444448888888888888888888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ171-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1i−ii−i1-11-1
χ181-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11−ii−ii-11-11
χ191-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i1-11-1−ii−ii-11-11
χ201-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−ii-11-11i−ii−i1-11-1
χ211-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11i−ii−i-11-11
χ221-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1−ii−ii1-11-1
χ231-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i-11-11−ii−ii1-11-1
χ241-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−ii1-11-1i−ii−i-11-11
χ251-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii1-1-11-111-1i−i−ii
χ261-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−i-111-11-1-11−iii−i
χ271-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−ii1-1-111-1-11−iii−i
χ281-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i-111-1-111-1i−i−ii
χ291-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−ii-111-1-111-1−iii−i
χ301-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i1-1-111-1-11i−i−ii
χ311-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii-111-11-1-11i−i−ii
χ321-1-11-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−i1-1-11-111-1−iii−i
χ332222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-222-2-222-2-222-2-2-2-2-2-2220000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ362222222222222222-2-2-2-2-2-222-2-222-2-222-2-2-2-2-2-22200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ372222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-222-2-222-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-222-2-222-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-2-2-22200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-2-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222222222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ4522-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ4622-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−200−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ4722-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ4822-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−2200−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ4922-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i22−2−222−2−222ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ5022-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i22−2−222−2−22−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ00−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ5122-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2−222−2−222−22ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ00−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ5222-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2−222−2−222−2−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ5322-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ31−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ5422-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−2200−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ5522-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ5622-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−200−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ31−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ5722-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2−222−2−222−22ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ5822-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2−222−2−222−2−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ300−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ5922-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i22−2−222−2−222ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ300−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ6022-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i22−2−222−2−22−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ612-22-2-222-22i−2i−2i2i2i−2i−2i2i000000002-200-2200−2i2i002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
χ622-22-2-222-22i−2i−2i2i2i−2i−2i2i000000002-200-2200−2i2i002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i200−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ632-22-2-222-22i−2i−2i2i2i−2i−2i2i000000002-200-2200−2i2i002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ642-22-2-222-22i−2i−2i2i2i−2i−2i2i000000002-200-2200−2i2i002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i200−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
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χ1044-4-4444-4-4-4-4-4-44444-444-44-4000000000000-4400000000000000000000000000000000000000000000000000000000000000000000

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