Finite Group Databasebeta

← Group #367666

Character table — Group #367666

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444222222444444444444444444444422444444444444444444888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ171111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i1-111-1-11-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−i11-1-11-1i−ii−i1-1
χ181111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i1-111-1-11-1ii−i−i−i−iii-1-111ii−i−iii−i−i−i−iii-1-111-11−ii−ii-11
χ191111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-111-11ii−i−iii−i−i11-1-1−i−iii−i−iiiii−i−i11-1-1-11−ii−ii-11
χ201111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-111-11ii−i−i−i−iii-1-111−i−iii−i−iii−i−iii-1-1111-1i−ii−i1-1
χ211111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiii1-111-1-11-1−i−iiiii−i−i-1-111−i−iii−i−iiiii−i−i-1-111-11i−ii−i-11
χ221111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiii1-111-1-11-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii11-1-11-1−ii−ii1-1
χ231111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-111-11−i−iiiii−i−i-1-111ii−i−iii−i−iii−i−i-1-1111-1−ii−ii1-1
χ241111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-111-11−i−iii−i−iii11-1-1ii−i−iii−i−i−i−iii11-1-1-11i−ii−i-11
χ251111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i1-1-1-1111-1−i−iiiii−i−i11-1-1ii−i−i−i−iii−i−iii-1-111-11i−i−ii1-1
χ261111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i1-1-1-1111-1−i−iii−i−iii-1-111ii−i−i−i−iiiii−i−i11-1-11-1−iii−i-11
χ271111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i-1111-1-1-11−i−iiiii−i−i11-1-1−i−iiiii−i−i−i−iii-1-1111-1−iii−i-11
χ281111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i-1111-1-1-11−i−iii−i−iii-1-111−i−iiiii−i−iii−i−i11-1-1-11i−i−ii1-1
χ291111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii1-1-1-1111-1ii−i−iii−i−i-1-111−i−iiiii−i−i−i−iii11-1-11-1i−i−ii-11
χ301111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii1-1-1-1111-1ii−i−i−i−iii11-1-1−i−iiiii−i−iii−i−i-1-111-11−iii−i1-1
χ311111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii-1111-1-1-11ii−i−iii−i−i-1-111ii−i−i−i−iii−i−iii11-1-1-11−iii−i1-1
χ321111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii-1111-1-1-11ii−i−i−i−iii11-1-1ii−i−i−i−iiiii−i−i-1-1111-1i−i−ii-11
χ3322222222-2-222-2-22-2-2-22-20000000022-2-222-2-22-20000-220000000000002-22-200000000000000000000
χ3422222222-2-222-2-22-2-2-22-20000000022-2-222-2-2-2200002-2000000000000-22-2200000000000000000000
χ3522222222-2-222-2-22-2-2-22-200000000-2-222-2-2222-20000-22000000000000-22-2200000000000000000000
χ3622222222-2-222-2-22-2-2-22-200000000-2-222-2-222-2200002-20000000000002-22-200000000000000000000
χ3722222222-2-2-2-222-22-2-2-2222-2-222-2-2000000000000000000002-22-20000000000002-22-2000000000000
χ3822222222-2-2-2-222-22-2-2-2222-2-222-2-200000000000000000000-22-22000000000000-22-22000000000000
χ3922222222-2-2-2-222-22-2-2-22-2-222-2-222000000000000000000002-22-2000000000000-22-22000000000000
χ4022222222-2-2-2-222-22-2-2-22-2-222-2-22200000000000000000000-22-220000000000002-22-2000000000000
χ412222-2-2-2-2-2-222-2-2-2222-2222-2-2-2-222000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000
χ422222-2-2-2-2-2-222-2-2-2222-2222-2-2-2-22200000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000
χ432222-2-2-2-2-2-222-2-2-2222-22-2-22222-2-2000000000000000000002i−2i−2i2i000000000000−2i2i2i−2i000000000000
χ442222-2-2-2-2-2-222-2-2-2222-22-2-22222-2-200000000000000000000−2i2i2i−2i0000000000002i−2i−2i2i000000000000
χ452222-2-2-2-2-2-2-2-2222-2222-2000000002i2i−2i−2i−2i−2i2i2i220000-2-20000000000002i−2i−2i2i00000000000000000000
χ462222-2-2-2-2-2-2-2-2222-2222-2000000002i2i−2i−2i−2i−2i2i2i-2-2000022000000000000−2i2i2i−2i00000000000000000000
χ472222-2-2-2-2-2-2-2-2222-2222-200000000−2i−2i2i2i2i2i−2i−2i220000-2-2000000000000−2i2i2i−2i00000000000000000000
χ482222-2-2-2-2-2-2-2-2222-2222-200000000−2i−2i2i2i2i2i−2i−2i-2-20000220000000000002i−2i−2i2i00000000000000000000
χ492-2-2222-2-22-22-22-22-22-2-22000000002-22-22-22-2002i−2i2i−2i0000000000000000002i−2i2i−2i0000000000000000
χ502-2-2222-2-22-22-22-22-22-2-22000000002-22-22-22-200−2i2i−2i2i000000000000000000−2i2i−2i2i0000000000000000
χ512-2-2222-2-22-22-22-22-22-2-2200000000-22-22-22-22002i−2i2i−2i000000000000000000−2i2i−2i2i0000000000000000
χ522-2-2222-2-22-22-22-22-22-2-2200000000-22-22-22-2200−2i2i−2i2i0000000000000000002i−2i2i−2i0000000000000000
χ532-2-2222-2-22-2-22-22-222-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2i−2i0000000000002-22-200000000
χ542-2-2222-2-22-2-22-22-222-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i−2i2i000000000000-22-2200000000
χ552-2-2222-2-22-2-22-22-222-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i2i−2i000000000000-22-2200000000
χ562-2-2222-2-22-2-22-22-222-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i−2i2i0000000000002-22-200000000
χ572-2-2222-2-2-222-2-2222-22-2-22i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000002i−2i2i−2i00000000000000000000000000000000
χ582-2-2222-2-2-222-2-2222-22-2-22i−2i−2i2i2i−2i−2i2i-222-2-222-200000000−2i2i−2i2i00000000000000000000000000000000
χ592-2-2222-2-2-222-2-2222-22-2-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-2200000000−2i2i−2i2i00000000000000000000000000000000
χ602-2-2222-2-2-222-2-2222-22-2-2−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000002i−2i2i−2i00000000000000000000000000000000
χ612-2-22-2-2222-22-22-2-22-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000002i−2i−2i2i0000000000002-2-2200000000
χ622-2-22-2-2222-22-22-2-22-222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000−2i2i2i−2i000000000000-222-200000000
χ632-2-22-2-2222-22-22-2-22-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000002i−2i−2i2i000000000000-222-200000000
χ642-2-22-2-2222-22-22-2-22-222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000−2i2i2i−2i0000000000002-2-2200000000
χ652-2-22-2-2222-2-22-222-2-22-22000000002i−2i2i−2i−2i2i−2i2i002i−2i−2i2i000000000000000000-222-20000000000000000
χ662-2-22-2-2222-2-22-222-2-22-22000000002i−2i2i−2i−2i2i−2i2i00−2i2i2i−2i0000000000000000002-2-220000000000000000
χ672-2-22-2-2222-2-22-222-2-22-2200000000−2i2i−2i2i2i−2i2i−2i002i−2i−2i2i0000000000000000002-2-220000000000000000
χ682-2-22-2-2222-2-22-222-2-22-2200000000−2i2i−2i2i2i−2i2i−2i00−2i2i2i−2i000000000000000000-222-20000000000000000
χ692-2-22-2-222-22-222-2222-2-2-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000-222-200000000000000000000000000000000
χ702-2-22-2-222-22-222-2222-2-2-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000002-2-2200000000000000000000000000000000
χ712-2-22-2-222-22-222-2222-2-2-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000002-2-2200000000000000000000000000000000
χ722-2-22-2-222-22-222-2222-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000-222-200000000000000000000000000000000
χ734444444444-4-4-4-4-4-444-4-4000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-4-4-44-444-4-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-444-4-44-4-44-444000000000000000000000000000000000000000000000000000000000000
χ7788-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ798-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).