Finite Group Databasebeta

← Group #162446

Character table — Group #162446

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444888888882444888888888888888888888888888822244444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1111-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-1-11-1-111
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1iiii−i−i−i−i11-1-1−i−iiiii−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-111-111-1-1
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1−i−i−i−iiiii11-1-1ii−i−i−i−iii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-111-111-1-1
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-1-11-1-111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii1111-1-1-1-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-1-1-11111
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i−i−i−i−iiiii-1-1-1-11111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i-111-1ii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−i-11-11-111-1
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i-111-1−i−iii−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iii1-11-11-1-11
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiii-111-1ii−i−iii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-11-1-11
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiii-111-1−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii-11-11-111-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i1-1-11ii−i−i−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-1-111-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i1-1-11−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i11-1-11-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii1-1-11ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii11-1-11-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii1-1-11−i−iiiii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-1-111-11-11
χ2511111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-11-111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111-11-1
χ2611111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-11-11
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-11-11
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-1-11111-1-11111-1-1-1-1111-11-1
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111111-11-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-111-1-11
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111-11-1-111-1
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-111-1-1-1-1-1-11111-1-11-11-1-111-1
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-11-111-1-11
χ332222222222222222-2-22222-2-22222-2-2-2-2-2-2222200000000-2-2-2-2000000000000000000000000000000000000
χ342222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-22222-2-200000000-2-222000000000000000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-222-2-222-2-2-2-222-2-2220000000022-2-2000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-2-2-222000000002-2-22000000000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-222-2-222-2-222-2-222-2-200000000-222-2000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-22222-2-2-2-2000000002-22-2000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000-22-22000000000000000000000000000000000000
χ4122-222-2-2-222-2-22i2i−2i−2i002i2i−2i−2i002i−2i2-20000002i−2i2-20000000000001+i−1−i1−i−1+i0000000000001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4222-222-2-2-222-2-22i2i−2i−2i002i2i−2i−2i002i−2i2-20000002i−2i2-2000000000000−1−i1+i−1+i1−i000000000000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4322-222-2-2-222-2-22i2i−2i−2i002i2i−2i−2i00−2i2i-22000000−2i2i-220000000000001+i−1−i1−i−1+i0000000000001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4422-222-2-2-222-2-22i2i−2i−2i002i2i−2i−2i00−2i2i-22000000−2i2i-22000000000000−1−i1+i−1+i1−i000000000000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4522-222-2-2-222-2-2−2i−2i2i2i00−2i−2i2i2i002i−2i-220000002i−2i-220000000000001−i−1+i1+i−1−i0000000000001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4622-222-2-2-222-2-2−2i−2i2i2i00−2i−2i2i2i002i−2i-220000002i−2i-22000000000000−1+i1−i−1−i1+i000000000000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4722-222-2-2-222-2-2−2i−2i2i2i00−2i−2i2i2i00−2i2i2-2000000−2i2i2-20000000000001−i−1+i1+i−1−i0000000000001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4822-222-2-2-222-2-2−2i−2i2i2i00−2i−2i2i2i00−2i2i2-2000000−2i2i2-2000000000000−1+i1−i−1−i1+i000000000000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4922-222-2-2-2-2-2222i2i−2i−2i00−2i−2i2i2i002i−2i-22000000−2i2i2-20000000000001−i−1+i1+i−1−i000000000000−1+i1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ5022-222-2-2-2-2-2222i2i−2i−2i00−2i−2i2i2i002i−2i-22000000−2i2i2-2000000000000−1+i1−i−1−i1+i0000000000001−i−1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ5122-222-2-2-2-2-2222i2i−2i−2i00−2i−2i2i2i00−2i2i2-20000002i−2i-220000000000001−i−1+i1+i−1−i000000000000−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ5222-222-2-2-2-2-2222i2i−2i−2i00−2i−2i2i2i00−2i2i2-20000002i−2i-22000000000000−1+i1−i−1−i1+i0000000000001−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ5322-222-2-2-2-2-222−2i−2i2i2i002i2i−2i−2i002i−2i2-2000000−2i2i-220000000000001+i−1−i1−i−1+i000000000000−1−i1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ5422-222-2-2-2-2-222−2i−2i2i2i002i2i−2i−2i002i−2i2-2000000−2i2i-22000000000000−1−i1+i−1+i1−i0000000000001+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ5522-222-2-2-2-2-222−2i−2i2i2i002i2i−2i−2i00−2i2i-220000002i−2i2-20000000000001+i−1−i1−i−1+i000000000000−1−i1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ5622-222-2-2-2-2-222−2i−2i2i2i002i2i−2i−2i00−2i2i-220000002i−2i2-2000000000000−1−i1+i−1+i1−i0000000000001+i−1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ572-222-22-2-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00002-22-22i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ582-222-22-2-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00002-22-22i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ592-222-22-2-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i0000-22-22−2i2i00002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ602-222-22-2-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i0000-22-22−2i2i0000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ612-222-22-2-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i0000-22-222i−2i00002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ622-222-22-2-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i0000-22-222i−2i0000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ632-222-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00002-22-2−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ642-222-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00002-22-2−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ652-222-22-2-2-22-222i−2i2i−2i2i−2i−2i2i−2i2i2i−2i0000-222-2−2i2i00002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ662-222-22-2-2-22-222i−2i2i−2i2i−2i−2i2i−2i2i2i−2i0000-222-2−2i2i0000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ672-222-22-2-2-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00002-2-222i−2i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ682-222-22-2-2-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00002-2-222i−2i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ692-222-22-2-2-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00002-2-22−2i2i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ702-222-22-2-2-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00002-2-22−2i2i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ712-222-22-2-2-22-22−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i0000-222-22i−2i00002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ722-222-22-2-2-22-22−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i0000-222-22i−2i0000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ73444-4-4-44-4000000004i−4i0000−4i4i000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000
χ74444-4-4-44-4000000004i−4i0000−4i4i00000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000000000000000000000000
χ75444-4-4-44-400000000−4i4i00004i−4i000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000000000000000000000000
χ76444-4-4-44-400000000−4i4i00004i−4i00000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000000000000000000000
χ774-44-44-4-4400000000440000-4-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ784-44-44-4-4400000000440000-4-400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ794-44-44-4-4400000000-4-40000440000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ804-44-44-4-4400000000-4-400004400000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ814-4-44-4-4444-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000
χ824-4-44-4-4444-4-44-444-400-444-40000000000000000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-444-44-4-4400-444-40000000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-444-4-444-4004-4-440000000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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