Finite Group Databasebeta

← Group #147487

Character table — Group #147487

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order122222222244444444888888888888888888444444444444888888881616161616161616161616161616161644448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1iiii−i−i−i−i11111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ10111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1iiii−i−i−i−i11111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ11111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1iiii−i−i−i−i1-1-1-1-11111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ12111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1iiii−i−i−i−i1-1-1-1-11111ii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ13111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1−i−i−i−iiiii11111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ14111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1−i−i−i−iiiii11111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ15111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1−i−i−i−iiiii1-1-1-1-11111−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ16111111-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1−i−i−i−iiiii1-1-1-1-11111−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ171-1-111-111-1-11-1-111-11-1-1-11111-11-1ii−i−iii−i−i-1ii−i−iii−i−ii−ii−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181-1-111-111-1-11-1-111-11-1-1-11111-11-1ii−i−iii−i−i-1ii−i−iii−i−ii−ii−i11-1-111-1-1-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191-1-111-111-1-11-1-111-11-1-1-11111-11-1ii−i−iii−i−i-1−i−iii−i−iiii−ii−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201-1-111-111-1-11-1-111-11-1-1-11111-11-1ii−i−iii−i−i-1−i−iii−i−iiii−ii−i-1-111-1-111-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211-1-111-111-1-11-1-111-11-1-1-11111-11-1−i−iii−i−iii-1ii−i−iii−i−i−ii−ii-1-111-1-11111-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ221-1-111-111-1-11-1-111-11-1-1-11111-11-1−i−iii−i−iii-1ii−i−iii−i−i−ii−ii-1-111-1-111-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ231-1-111-111-1-11-1-111-11-1-1-11111-11-1−i−iii−i−iii-1−i−iii−i−iii−ii−ii11-1-111-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ241-1-111-111-1-11-1-111-11-1-1-11111-11-1−i−iii−i−iii-1−i−iii−i−iii−ii−ii11-1-111-1-1-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ251-1-111-1-1-1111-1-1-111-1111-1-111-1-1111-1-1-1-111-1ii−i−i−i−iii1-1-11−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ261-1-111-1-1-1111-1-1-111-1111-1-111-1-1111-1-1-1-111-1ii−i−i−i−iii1-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ271-1-111-1-1-1111-1-1-111-1111-1-111-1-1111-1-1-1-111-1−i−iiiii−i−i1-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ281-1-111-1-1-1111-1-1-111-1111-1-111-1-1111-1-1-1-111-1−i−iiiii−i−i1-1-11ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ291-1-111-1-1-1111-1-1-111-1111-1-111-1-11-1-11111-1-1-1ii−i−i−i−iii-111-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ301-1-111-1-1-1111-1-1-111-1111-1-111-1-11-1-11111-1-1-1ii−i−i−i−iii-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ311-1-111-1-1-1111-1-1-111-1111-1-111-1-11-1-11111-1-1-1−i−iiiii−i−i-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ321-1-111-1-1-1111-1-1-111-1111-1-111-1-11-1-11111-1-1-1−i−iiiii−i−i-111-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
χ33222222222222222222-2-2-2-2-2-2-2-2-222222222-200000000-2-2-2-200000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-20000000002i−2i2i−2i2i−2i2i−2i000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ362222222222-2-2-2-2-2-2-2-20000000002i−2i2i−2i2i−2i2i−2i000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ372222222222-2-2-2-2-2-2-2-2000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ382222222222-2-2-2-2-2-2-2-2000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ39222222-2-2-2-2222-22-2-2-22222-2-2-2222i2i2i2i−2i−2i−2i−2i-200000000−2i−2i2i2i00000000000000000000000000000000
χ40222222-2-2-2-2222-22-2-2-22222-2-2-222−2i−2i−2i−2i2i2i2i2i-2000000002i2i−2i−2i00000000000000000000000000000000
χ41222222-2-2-2-2-2-2-22-22220000000002-22-2-22-220000000000000000000002−22−2−22−222−22−2−22−2200000000
χ42222222-2-2-2-2-2-2-22-22220000000002-22-2-22-22000000000000000000000−22−222−22−2−22−222−22−200000000
χ43222222-2-2-2-2-2-2-22-2222000000000-22-222-22-20000000000000000000002−22−2−22−22−22−222−22−200000000
χ44222222-2-2-2-2-2-2-22-2222000000000-22-222-22-2000000000000000000000−22−222−22−22−22−2−22−2200000000
χ452222-2-22-22-2-22-222-2-2222222-2-2-2-20000000022-22-22-22-2000000000000000000000000000000000000
χ462222-2-22-22-2-22-222-2-2222222-2-2-2-2000000002-22-22-22-22000000000000000000000000000000000000
χ472222-2-22-22-2-22-222-2-22-2-2-2-2-2222200000000-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ482222-2-22-22-2-22-222-2-22-2-2-2-2-2222200000000-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ492222-2-2-22-22-22-2-2222-22222-222-2-200000000-20000000000002-22-2-22-22000000000000000000000000
χ502222-2-2-22-22-22-2-2222-22222-222-2-200000000-2000000000000-22-222-22-2000000000000000000000000
χ512222-2-2-22-22-22-2-2222-2-2-2-2-22-2-2220000000022-22-2-22-22000000000000000000000000000000000000
χ522222-2-2-22-22-22-2-2222-2-2-2-2-22-2-222000000002-22-222-22-2000000000000000000000000000000000000
χ532-2-222-222-2-22-2-222-22-222-2-2-2-22-222i2i−2i−2i2i2i−2i−2i200000000−2i2i−2i2i00000000000000000000000000000000
χ542-2-222-222-2-22-2-222-22-222-2-2-2-22-22−2i−2i2i2i−2i−2i2i2i2000000002i−2i2i−2i00000000000000000000000000000000
χ552-2-222-222-2-2-222-2-22-220000000002-2-222-2-22000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ562-2-222-222-2-2-222-2-22-220000000002-2-222-2-22000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ572-2-222-222-2-2-222-2-22-22000000000-222-2-222-2000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ582-2-222-222-2-2-222-2-22-22000000000-222-2-222-2000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ592-2-222-2-2-2222-2-2-222-22-2-222-2-222-222-2-2-2-222200000000-222-200000000000000000000000000000000
χ602-2-222-2-2-2222-2-2-222-22-2-222-2-222-2-2-22222-2-22000000002-2-2200000000000000000000000000000000
χ612-2-222-2-2-222-2222-2-22-20000000002i−2i−2i2i−2i2i2i−2i0000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ622-2-222-2-2-222-2222-2-22-20000000002i−2i−2i2i−2i2i2i−2i000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ632-2-222-2-2-222-2222-2-22-2000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ642-2-222-2-2-222-2222-2-22-2000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ652-2-22-222-2-22-2-22222-2-222-2-2-22-22-20000000020000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ662-2-22-222-2-22-2-22222-2-222-2-2-22-22-2000000002000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ672-2-22-222-2-22-2-22222-2-2-2-2222-22-2200000000-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ682-2-22-222-2-22-2-22222-2-2-2-2222-22-2200000000-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ692-2-22-22-222-2-2-22-22-22222-2-22-222-200000000-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ702-2-22-22-222-2-2-22-22-22222-2-22-222-200000000-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ712-2-22-22-222-2-2-22-22-222-2-222-22-2-220000000020000000000002-2-22-222-2000000000000000000000000
χ722-2-22-22-222-2-2-22-22-222-2-222-22-2-22000000002000000000000-222-22-2-22000000000000000000000000
χ734444-4-44-44-44-44-4-444-400000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-44-444-444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ754-4-44-444-4-4444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ764-4-44-44-444-444-44-44-4-400000000000000000000000000000000000000000000000000000000000000
χ7788-8-80000000000000042−4242−420000000000000000000000000000000000000000000000000000000000
χ7888-8-800000000000000−4242−42420000000000000000000000000000000000000000000000000000000000
χ798-88-80000000000000042−42−42420000000000000000000000000000000000000000000000000000000000
χ808-88-800000000000000−424242−420000000000000000000000000000000000000000000000000000000000

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