Finite Group Databasebeta

← Group #10818

Character table — Group #10818

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order1222222244444444222244444444444444444444888888888888888888888888888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111iiiiiiii−i−i−i−i−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1-1-111−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-1-11111-1-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−i−i−i−i−iiiiiiiii1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i
χ171111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ181111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ191111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ201111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ211111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii−ii−iii−ii−i
χ221111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−ii−ii−i−ii−ii
χ231111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i−ii−ii−ii−ii
χ241111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−ii−ii−iii−ii−ii−ii−i
χ251111-1-1-1-1-1-1-1-11111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii-111-1-111-1
χ261111-1-1-1-1-1-1-1-11111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i−iii−i1-1-111-1-11
χ271111-1-1-1-1-1-1-1-11111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii−iii−i-111-11-1-11
χ281111-1-1-1-1-1-1-1-11111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−ii−i−ii1-1-11-111-1
χ291111-1-1-1-1-1-1-1-11111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−ii−iii−i1-1-11-111-1
χ301111-1-1-1-1-1-1-1-11111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−ii−i−ii-111-11-1-11
χ311111-1-1-1-1-1-1-1-11111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii1-1-111-1-11
χ321111-1-1-1-1-1-1-1-11111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i−iii−i-111-1-111-1
χ332222222222222222-2-2-2-2-2-2-20000000000000000-222-2-222-2-222-2-222-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-20000000000000000-2-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222-2-2-20000000000000000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2-222-2-2220000000000000000-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ382222-2-2-2-22222-2-2-2-2-222-2-2220000000000000000-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ392222-2-2-2-2-2-2-2-222222-2-22-2220000000000000000-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ402222-2-2-2-2-2-2-2-222222-2-22-2220000000000000000-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4122-2-222-2-22i−2i2i−2i2i2i−2i−2i00000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζi2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ4222-2-222-2-22i−2i2i−2i2i2i−2i−2i00000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ4322-2-222-2-22i−2i2i−2i2i2i−2i−2i0000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ4422-2-222-2-22i−2i2i−2i2i2i−2i−2i0000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζi2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ4522-2-222-2-2−2i2i−2i2i−2i−2i2i2i00000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ4622-2-222-2-2−2i2i−2i2i−2i−2i2i2i00000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ4722-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ4822-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ4922-2-2-2-2222i−2i2i−2i−2i−2i2i2i00000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζi2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ5022-2-2-2-2222i−2i2i−2i−2i−2i2i2i00000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ5122-2-2-2-2222i−2i2i−2i−2i−2i2i2i0000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ5222-2-2-2-2222i−2i2i−2i−2i−2i2i2i0000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζi2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ5322-2-2-2-222−2i2i−2i2i2i2i−2i−2i00000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0002ζ−2ζ00−2ζ2ζ002ζ3−2ζ300−2ζ32ζ3i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ5422-2-2-2-222−2i2i−2i2i2i2i−2i−2i00000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000−2ζ2ζ002ζ−2ζ00−2ζ32ζ3002ζ3−2ζ3−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ5522-2-2-2-222−2i2i−2i2i2i2i−2i−2i0000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0002ζ−2ζ00−2ζ2ζ002ζ3−2ζ300−2ζ32ζ3−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ5622-2-2-2-222−2i2i−2i2i2i2i−2i−2i0000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000−2ζ2ζ002ζ−2ζ00−2ζ32ζ3002ζ3−2ζ3i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ572-22-22-22-22i−2i−2i2i2i−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−i02ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ582-22-22-22-22i−2i−2i2i2i−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−i0−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ00−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ592-22-22-22-22i−2i−2i2i2i−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+i02ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ00−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ602-22-22-22-22i−2i−2i2i2i−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+i0−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ612-22-22-22-2−2i2i2i−2i−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+i02ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ300−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ622-22-22-22-2−2i2i2i−2i−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+i0−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ632-22-22-22-2−2i2i2i−2i−2i2i−2i2i0000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i02ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ642-22-22-22-2−2i2i2i−2i−2i2i−2i2i0000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ300−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ652-22-2-22-222i−2i−2i2i−2i2i−2i2i00000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i02ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ662-22-2-22-222i−2i−2i2i−2i2i−2i2i00000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ00−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ672-22-2-22-222i−2i−2i2i−2i2i−2i2i0000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i02ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ00−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ682-22-2-22-222i−2i−2i2i−2i2i−2i2i0000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ692-22-2-22-22−2i2i2i−2i2i−2i2i−2i00000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i02ζ−2ζ00−2ζ2ζ002ζ3−2ζ300−2ζ32ζ300−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ702-22-2-22-22−2i2i2i−2i2i−2i2i−2i00000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0−2ζ2ζ002ζ−2ζ00−2ζ32ζ3002ζ3−2ζ3002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
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χ732-2-222-2-2222-2-22-2-2222-2-2-22-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2000000000000000000000000000000000000000000000000
χ742-2-222-2-2222-2-22-2-2222-2-2-22-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2000000000000000000000000000000000000000000000000
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χ802-2-222-2-22-2-222-222-2-2-222-22-2-222-2-222-2-222-2-222-22000000000000000000000000000000000000000000000000
χ812-2-22-222-222-2-2-222-22-22-2-2-222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2000000000000000000000000000000000000000000000000
χ822-2-22-222-222-2-2-222-22-22-2-2-22−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2000000000000000000000000000000000000000000000000
χ832-2-22-222-222-2-2-222-2-22-2222-20000000000000000-200000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ842-2-22-222-222-2-2-222-2-22-2222-20000000000000000-20000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ852-2-22-222-2-2-2222-2-222-22-222-20000000000000000-200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ862-2-22-222-2-2-2222-2-222-22-222-20000000000000000-20000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ872-2-22-222-2-2-2222-2-22-22-22-2-222-2-22-222-22-2-22-222-22000000000000000000000000000000000000000000000000
χ882-2-22-222-2-2-2222-2-22-22-22-2-22-222-22-2-22-222-22-2-222000000000000000000000000000000000000000000000000

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