Finite Group Databasebeta

← Group #376138

Character table — Group #376138

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444222222444444444444448888888822222244444444444444444488888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111
χ171-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1ii−i−iii−i−i1-11-11-1ii−i−i11-1-111-1-1ii−i−i1-1i−ii−i1-1
χ181-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−iiiii−i−i−i−i1-11-1-11ii−i−iii−i−i1-11-1-11−i−iii-1-11111-1-1−i−iii-11−ii−ii-11
χ191-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−iiiii−i−i−i−i-11-111-1−i−iii−i−iii-11-111-1ii−i−i11-1-111-1-1ii−i−i-11−ii−ii-11
χ201-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11−i−iii−i−iii-11-11-11−i−iii-1-11111-1-1−i−iii1-1i−ii−i1-1
χ211-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−i−i−i−i−iiiii1-1-111-1ii−i−i−i−iii1-1-111-1ii−i−i-1-111-1-111−i−iii1-1i−i−ii-11
χ221-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-11ii−i−i−i−iii1-1-11-11−i−iii11-1-1-1-111ii−i−i-11−iii−i1-1
χ231-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−i−i−i−i−iiiii-111-11-1−i−iiiii−i−i-111-11-1ii−i−i-1-111-1-111−i−iii-11−iii−i1-1
χ241-1-11-1-111111-1-1-111-1-11-1iiii−i−i−i−i−i−i−i−iiiii-111-1-11−i−iiiii−i−i-111-1-11−i−iii11-1-1-1-111ii−i−i1-1i−i−ii-11
χ251-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1−i−iiiii−i−i1-1-111-1−i−iii-1-111-1-111ii−i−i1-1−iii−i-11
χ261-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-11−i−iiiii−i−i1-1-11-11ii−i−i11-1-1-1-111−i−iii-11i−i−ii1-1
χ271-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiiiiiii−i−i−i−i-111-11-1ii−i−i−i−iii-111-11-1−i−iii-1-111-1-111ii−i−i-11i−i−ii1-1
χ281-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-11ii−i−i−i−iii-111-1-11ii−i−i11-1-1-1-111−i−iii1-1−iii−i-11
χ291-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−i−iii−i−iii1-11-11-1−i−iii11-1-111-1-1−i−iii1-1−ii−ii1-1
χ301-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiii−i−i−i−iiiii1-11-1-11−i−iii−i−iii1-11-1-11ii−i−i-1-11111-1-1ii−i−i-11i−ii−i-11
χ311-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiii−i−i−i−iiiii-11-111-1ii−i−iii−i−i-11-111-1−i−iii11-1-111-1-1−i−iii-11i−ii−i-11
χ321-1-11-1-111111-1-1-111-1-11-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11ii−i−iii−i−i-11-11-11ii−i−i-1-11111-1-1ii−i−i1-1−ii−ii1-1
χ33222222222-2-22-2-2-2-2-2-22222-2-222-2-222-2-222-2-200000000000000000000000000002-22-2000000000000
χ34222222222-2-22-2-2-2-2-2-22222-2-222-2-2-2-222-2-2220000000000000000000000000000-22-22000000000000
χ35222222222-2-22-2-2-2-2-2-222-2-222-2-22222-2-222-2-20000000000000000000000000000-22-22000000000000
χ36222222222-2-22-2-2-2-2-2-222-2-222-2-222-2-222-2-22200000000000000000000000000002-22-2000000000000
χ372222-2-2-2-2222222-2-2-2-2-2-22-22-22-22-200000000000022000000000000-2-22-22-200000000000000000000
χ382222-2-2-2-2222222-2-2-2-2-2-22-22-22-22-2000000000000-2-200000000000022-22-2200000000000000000000
χ392222-2-2-2-2222222-2-2-2-2-2-2-22-22-22-2200000000000022000000000000-2-2-22-2200000000000000000000
χ402222-2-2-2-2222222-2-2-2-2-2-2-22-22-22-22000000000000-2-2000000000000222-22-200000000000000000000
χ412222-2-2-2-22-2-22-2-22222-2-22-2-222-2-22000000000000000000000000000000002i−2i2i−2i00002i−2i2i−2i00000000
χ422222-2-2-2-22-2-22-2-22222-2-22-2-222-2-2200000000000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000
χ432222-2-2-2-22-2-22-2-22222-2-2-222-2-222-2000000000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i00000000
χ442222-2-2-2-22-2-22-2-22222-2-2-222-2-222-200000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i00000000
χ452222-2-2-2-2-22-2-22-22-22-222000000002-22-22-22-20022002-22-2000000-2-200000000000000000000000000
χ462222-2-2-2-2-22-2-22-22-22-222000000002-22-22-22-200-2-200-22-220000002200000000000000000000000000
χ472222-2-2-2-2-22-2-22-22-22-22200000000-22-22-22-22002200-22-22000000-2-200000000000000000000000000
χ482222-2-2-2-2-22-2-22-22-22-22200000000-22-22-22-2200-2-2002-22-20000002200000000000000000000000000
χ492222-2-2-2-2-2-22-2-22-22-2222000000002-2-222-2-2222000000002-22-2-2-20000000000000000000000000000
χ502222-2-2-2-2-2-22-2-22-22-2222000000002-2-222-2-22-2-200000000-22-22220000000000000000000000000000
χ512222-2-2-2-2-2-22-2-22-22-222200000000-222-2-222-22200000000-22-22-2-20000000000000000000000000000
χ522222-2-2-2-2-2-22-2-22-22-222200000000-222-2-222-2-2-2000000002-22-2220000000000000000000000000000
χ532-2-2222-2-2222-2-2-2-2-222-222i−2i2i−2i−2i2i−2i2i0000000000002-2000000000000-222i−2i−2i2i00000000000000000000
χ542-2-2222-2-2222-2-2-2-2-222-222i−2i2i−2i−2i2i−2i2i000000000000-220000000000002-2−2i2i2i−2i00000000000000000000
χ552-2-2222-2-2222-2-2-2-2-222-22−2i2i−2i2i2i−2i2i−2i0000000000002-2000000000000-22−2i2i2i−2i00000000000000000000
χ562-2-2222-2-2222-2-2-2-2-222-22−2i2i−2i2i2i−2i2i−2i000000000000-220000000000002-22i−2i−2i2i00000000000000000000
χ572-2-2222-2-22-2-2-22222-2-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000002i−2i−2i2i0000-222-200000000
χ582-2-2222-2-22-2-2-22222-2-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i00002-2-2200000000
χ592-2-2222-2-22-2-2-22222-2-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000002i−2i−2i2i00002-2-2200000000
χ602-2-2222-2-22-2-2-22222-2-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000−2i2i2i−2i0000-222-200000000
χ612-2-2222-2-2-22-22-222-2-222-2000000002i−2i2i−2i−2i2i−2i2i002-2002i−2i−2i2i000000-2200000000000000000000000000
χ622-2-2222-2-2-22-22-222-2-222-2000000002i−2i2i−2i−2i2i−2i2i00-2200−2i2i2i−2i0000002-200000000000000000000000000
χ632-2-2222-2-2-22-22-222-2-222-200000000−2i2i−2i2i2i−2i2i−2i002-200−2i2i2i−2i000000-2200000000000000000000000000
χ642-2-2222-2-2-22-22-222-2-222-200000000−2i2i−2i2i2i−2i2i−2i00-22002i−2i−2i2i0000002-200000000000000000000000000
χ652-2-2222-2-2-2-2222-2-222-22-2000000002i−2i−2i2i−2i2i2i−2i2-2000000002i−2i−2i2i-220000000000000000000000000000
χ662-2-2222-2-2-2-2222-2-222-22-2000000002i−2i−2i2i−2i2i2i−2i-2200000000−2i2i2i−2i2-20000000000000000000000000000
χ672-2-2222-2-2-2-2222-2-222-22-200000000−2i2i2i−2i2i−2i−2i2i2-200000000−2i2i2i−2i-220000000000000000000000000000
χ682-2-2222-2-2-2-2222-2-222-22-200000000−2i2i2i−2i2i−2i−2i2i-22000000002i−2i−2i2i2-20000000000000000000000000000
χ692-2-22-2-2222-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000002-2-22000000000000
χ702-2-22-2-2222-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000-222-2000000000000
χ712-2-22-2-2222-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000-222-2000000000000
χ722-2-22-2-2222-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002-2-22000000000000
χ7344444444-44-4-44-4-44-44-4-4000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-44-4-444-44-4-4-4000000000000000000000000000000000000000000000000000000000000
χ754-4-44-4-444-44-44-44-444-4-44000000000000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-4-4444-44-4-44-44000000000000000000000000000000000000000000000000000000000000
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).