Finite Group Databasebeta

← Group #375863

Character table — Group #375863

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222222222244444444444444448888888888888888888888888888888888888888161616161616
order12222222224444444444444444444444442222444444444444444488888888888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-111-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ171-11-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1i−i1-11-1ii−i−ii−i11-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−i
χ181-11-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1−ii1-11-1ii−i−i−ii-1-111ii−i−i11-1-1-1-111−i−iii−i−iii-11-11−ii
χ191-11-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-1-11i−i1-1-11−i−iiii−i11-1-1−i−iii-1-11111-1-1ii−i−i−i−iii-11-11−ii
χ201-11-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-1-11−ii1-1-11−i−iii−ii-1-111−i−iii-1-111-1-111−i−iiiii−i−i1-11-1i−i
χ211-11-11-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-111-1i−i-111-1ii−i−ii−i-1-111−i−iii-1-11111-1-1−i−iii−i−iii1-1-11i−i
χ221-11-11-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-111-1−ii-111-1ii−i−i−ii11-1-1−i−iii-1-111-1-111ii−i−iii−i−i-111-1−ii
χ231-11-11-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-11-11i−i-11-11−i−iiii−i-1-111ii−i−i11-1-111-1-1−i−iiiii−i−i-111-1−ii
χ241-11-11-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-11-11−ii-11-11−i−iii−ii11-1-1ii−i−i11-1-1-1-111ii−i−i−i−iii1-1-11i−i
χ251-11-11-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-111-1i−i-111-1−i−iiii−i11-1-1ii−i−i-1-111-1-111−i−iii−i−iii-111-1i−i
χ261-11-11-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-111-1−ii-111-1−i−iii−ii-1-111ii−i−i-1-11111-1-1ii−i−iii−i−i1-1-11−ii
χ271-11-11-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-11-11i−i-11-11ii−i−ii−i11-1-1−i−iii11-1-1-1-111−i−iiiii−i−i1-1-11−ii
χ281-11-11-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-11-11−ii-11-11ii−i−i−ii-1-111−i−iii11-1-111-1-1ii−i−i−i−iii-111-1i−i
χ291-11-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1i−i1-11-1−i−iiii−i-1-111−i−iii11-1-1-1-111ii−i−iii−i−i-11-11i−i
χ301-11-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1−ii1-11-1−i−iii−ii11-1-1−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii
χ311-11-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-1-11i−i1-1-11ii−i−ii−i-1-111ii−i−i-1-111-1-111ii−i−i−i−iii1-11-1−ii
χ321-11-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-1-11−ii1-1-11ii−i−i−ii11-1-1ii−i−i-1-11111-1-1−i−iiiii−i−i-11-11i−i
χ33222222-2-2-2-2-2-22222-2-22-22-22-22-22-22-22-22-2220000-2-200000000000000000000000000000000000000
χ34222222-2-2-2-2-2-22222-2-22-22-2-22-222-22-2-22-22-2-200002200000000000000000000000000000000000000
χ35222222-2-2-2-2-2-22222-2-2-22-222-22-2-22-222-22-2-2-200002200000000000000000000000000000000000000
χ36222222-2-2-2-2-2-22222-2-2-22-22-22-22-22-22-22-22220000-2-200000000000000000000000000000000000000
χ372222-2-22-22-22-22-22-22-2000022220000-2-2-2-200000000002-22-200000000002-22-2000000000000000000
χ382222-2-22-22-22-22-22-22-2000022220000-2-2-2-20000000000-22-220000000000-22-22000000000000000000
χ392222-2-22-22-22-22-22-22-20000-2-2-2-20000222200000000002-22-20000000000-22-22000000000000000000
χ402222-2-22-22-22-22-22-22-20000-2-2-2-2000022220000000000-22-2200000000002-22-2000000000000000000
χ412222-2-22-22-2-22-22-22-222-22-20000-22-22000000002200000000-2-20000000000002-22-200000000000000
χ422222-2-22-22-2-22-22-22-222-22-20000-22-2200000000-2-20000000022000000000000-22-2200000000000000
χ432222-2-22-22-2-22-22-22-22-22-2200002-22-2000000002200000000-2-2000000000000-22-2200000000000000
χ442222-2-22-22-2-22-22-22-22-22-2200002-22-200000000-2-200000000220000000000002-22-200000000000000
χ452222-2-2-22-222-2-22-222-222220000-2-2-2-2000000000000000000002-22-20000000000002-22-20000000000
χ462222-2-2-22-222-2-22-222-222220000-2-2-2-200000000000000000000-22-22000000000000-22-220000000000
χ472222-2-2-22-222-2-22-222-2-2-2-2-200002222000000000000000000002-22-2000000000000-22-220000000000
χ482222-2-2-22-222-2-22-222-2-2-2-2-20000222200000000000000000000-22-220000000000002-22-20000000000
χ492222-2-2-22-22-222-22-2-2200002-22-20000-22-2200220000-2-200000000002-22-20000000000000000000000
χ502222-2-2-22-22-222-22-2-2200002-22-20000-22-2200-2-20000220000000000-22-220000000000000000000000
χ512222-2-2-22-22-222-22-2-220000-22-2200002-22-200220000-2-20000000000-22-220000000000000000000000
χ522222-2-2-22-22-222-22-2-220000-22-2200002-22-200-2-200002200000000002-22-20000000000000000000000
χ532-22-22-222-2-2-2-222-2-2222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2-20000-2200000000000000000000000000000000000000
χ542-22-22-222-2-2-2-222-2-2222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i-2200002-200000000000000000000000000000000000000
χ552-22-22-222-2-2-2-222-2-222−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i-2200002-200000000000000000000000000000000000000
χ562-22-22-222-2-2-2-222-2-222−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2-20000-2200000000000000000000000000000000000000
χ572-22-2-222-2-222-2-222-2-222i2i−2i−2i0000−2i−2i2i2i000000000000000000002-2-220000000000002i−2i−2i2i0000000000
χ582-22-2-222-2-222-2-222-2-222i2i−2i−2i0000−2i−2i2i2i00000000000000000000-222-2000000000000−2i2i2i−2i0000000000
χ592-22-2-222-2-222-2-222-2-22−2i−2i2i2i00002i2i−2i−2i000000000000000000002-2-22000000000000−2i2i2i−2i0000000000
χ602-22-2-222-2-222-2-222-2-22−2i−2i2i2i00002i2i−2i−2i00000000000000000000-222-20000000000002i−2i−2i2i0000000000
χ612-22-2-222-2-22-222-2-222-200002i−2i−2i2i0000−2i2i2i−2i002-20000-2200000000002i−2i−2i2i0000000000000000000000
χ622-22-2-222-2-22-222-2-222-200002i−2i−2i2i0000−2i2i2i−2i00-2200002-20000000000−2i2i2i−2i0000000000000000000000
χ632-22-2-222-2-22-222-2-222-20000−2i2i2i−2i00002i−2i−2i2i002-20000-220000000000−2i2i2i−2i0000000000000000000000
χ642-22-2-222-2-22-222-2-222-20000−2i2i2i−2i00002i−2i−2i2i00-2200002-200000000002i−2i−2i2i0000000000000000000000
χ652-22-2-22-222-22-22-2-22-2200002i2i−2i−2i0000−2i−2i2i2i00000000002i−2i−2i2i00000000002-2-22000000000000000000
χ662-22-2-22-222-22-22-2-22-2200002i2i−2i−2i0000−2i−2i2i2i0000000000−2i2i2i−2i0000000000-222-2000000000000000000
χ672-22-2-22-222-22-22-2-22-220000−2i−2i2i2i00002i2i−2i−2i00000000002i−2i−2i2i0000000000-222-2000000000000000000
χ682-22-2-22-222-22-22-2-22-220000−2i−2i2i2i00002i2i−2i−2i0000000000−2i2i2i−2i00000000002-2-22000000000000000000
χ692-22-2-22-222-2-22-222-22-22i−2i−2i2i0000−2i2i2i−2i000000002i−2i00000000−2i2i0000000000002-2-2200000000000000
χ702-22-2-22-222-2-22-222-22-22i−2i−2i2i0000−2i2i2i−2i00000000−2i2i000000002i−2i000000000000-222-200000000000000
χ712-22-2-22-222-2-22-222-22-2−2i2i2i−2i00002i−2i−2i2i000000002i−2i00000000−2i2i000000000000-222-200000000000000
χ722-22-2-22-222-2-22-222-22-2−2i2i2i−2i00002i−2i−2i2i00000000−2i2i000000002i−2i0000000000002-2-2200000000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ754-44-44-444-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000
χ764-44-44-4-4-444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ7788-8-800000000000000000000000000000000000000000000000000000000000000000022−2222−22000000
χ7888-8-8000000000000000000000000000000000000000000000000000000000000000000−2222−2222000000
χ798-8-880000000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000
χ808-8-88000000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000

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