Finite Group Databasebeta

← Group #111145

Character table — Group #111145

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444222222444444444444448888888844444444888888888888888888888888888822448888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-11-1-1-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1
χ101111111111-1-1-1-11-1-1-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111
χ111111111111-1-1-1-11-1-1-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11-1-111
χ121111111111-1-1-1-11-1-1-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1
χ131111111111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111
χ141111111111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1
χ151111111111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1
χ161111111111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111
χ171111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-1-11i−ii−i
χ181111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-111-1−ii−ii
χ191111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1ii−i−iii−i−i-1-111-1-111i−ii−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-111-1−ii−ii
χ201111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1ii−i−iii−i−i-1-111-1-111i−ii−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-1-11i−ii−i
χ211111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-1-11−ii−ii
χ221111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-111-1i−ii−i
χ231111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1−i−iii−i−iii-1-111-1-111−ii−iiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-111-1i−ii−i
χ241111-1-1-1-1111111-1-1-1-1-1-111-1-11-11-1−i−iii−i−iii-1-111-1-111−ii−iiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-1-11−ii−ii
χ251111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11ii−i−i−i−iiiii−i−i−i−iiii−i−ii-1-11111-1-1ii−i−i−i−iii-1-11111-1-111-1-1i−i−ii
χ261111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11ii−i−i−i−iiiii−i−i−i−iiii−i−ii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-1-111−iii−i
χ271111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11ii−i−i−i−iii−i−iiiii−i−ii−i−ii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-1-111−iii−i
χ281111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11ii−i−i−i−iii−i−iiiii−i−ii−i−ii11-1-1-1-111−i−iiiii−i−i11-1-1-1-11111-1-1i−i−ii
χ291111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11−i−iiiii−i−iii−i−i−i−iii−iii−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-11111-1-1−iii−i
χ301111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11−i−iiiii−i−iii−i−i−i−iii−iii−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-1-111i−i−ii
χ311111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11−i−iiiii−i−i−i−iiiii−i−i−iii−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-1-111i−i−ii
χ321111-1-1-1-111-1-1-1-1-1111-1111-1-1-11-11−i−iiiii−i−i−i−iiiii−i−i−iii−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-111-1-1−iii−i
χ3322222222222222222222-2-2-2-2-2-2-2-22222222200000000-2-2-2-200000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ352222222222-2-2-2-22-2-2-22-2-2-2-2-222222222-2-2-2-200000000-2-22200000000000000000000000000000000
χ362222222222-2-2-2-22-2-2-22-2-2-2-2-22222-2-2-2-222220000000022-2-200000000000000000000000000000000
χ3722222222-2-222-2-2-222-2-2-22-22-22-2-22000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ3822222222-2-222-2-2-222-2-2-22-22-22-2-2200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ3922222222-2-222-2-2-222-2-2-2-22-22-222-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4022222222-2-222-2-2-222-2-2-2-22-22-222-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4122222222-2-2-2-222-2-2-22-222-22-2-222-2000000002-22-2-22-22000000000000000000000000000000000000
χ4222222222-2-2-2-222-2-2-22-222-22-2-222-200000000-22-222-22-2000000000000000000000000000000000000
χ4322222222-2-2-2-222-2-2-22-22-22-222-2-22000000000000000000002-22-2-22-22000000000000000000000000
χ4422222222-2-2-2-222-2-2-22-22-22-222-2-2200000000000000000000-22-222-22-2000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-2-2-2-2-222-22-222i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i00000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-2-2-222-22-22−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i00000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2222-22-2-2222-22-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i00000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2222-22-2-2222-22-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-222-2-22-2-22222-2-2222-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ502222-2-2-2-2-2-222-2-22-2-22222-2-2222-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ512222-2-2-2-2-2-222-2-22-2-2222-222-2-2-222000000000000000000002-2-222-2-22000000000000000000000000
χ522222-2-2-2-2-2-222-2-22-2-2222-222-2-2-22200000000000000000000-222-2-222-2000000000000000000000000
χ532222-2-2-2-2-2-2-2-222222-22-22-2-22-2-222000000002-2-22-222-2000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-222222-22-22-2-22-2-22200000000-222-22-2-22000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-222222-22-2-222-222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ562222-2-2-2-2-2-2-2-222222-22-2-222-222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ572-2-2222-2-22-22-22-222-2-2-22000000002i−2i2i−2i2i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ582-2-2222-2-22-22-22-222-2-2-22000000002i−2i2i−2i2i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ592-2-2222-2-22-22-22-222-2-2-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ602-2-2222-2-22-22-22-222-2-2-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ612-2-2222-2-22-2-22-222-222-2-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ622-2-2222-2-22-2-22-222-222-2-2000000002i−2i2i−2i−2i2i−2i2i00000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ632-2-2222-2-22-2-22-222-222-2-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ642-2-2222-2-22-2-22-222-222-2-200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ652-2-22-2-2222-22-22-2-2-2222-2000000002-2-222-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ662-2-22-2-2222-22-22-2-2-2222-2000000002-2-222-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ672-2-22-2-2222-22-22-2-2-2222-200000000-222-2-222-200000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ682-2-22-2-2222-22-22-2-2-2222-200000000-222-2-222-200000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ692-2-22-2-2222-2-22-22-22-2-222000000002-2-22-222-2000000000000000000002−2−22−222−2−222−22−2−2200000000
χ702-2-22-2-2222-2-22-22-22-2-222000000002-2-22-222-200000000000000000000−222−22−2−222−2−22−222−200000000
χ712-2-22-2-2222-2-22-22-22-2-22200000000-222-22-2-22000000000000000000002−2−22−222−22−2−22−222−200000000
χ722-2-22-2-2222-2-22-22-22-2-22200000000-222-22-2-2200000000000000000000−222−22−2−22−222−22−2−2200000000
χ734-4-4444-4-4-444-4-44-44-444-4000000000000000000000000000000000000000000000000000000000000
χ744-4-4444-4-4-44-444-4-4-44-444000000000000000000000000000000000000000000000000000000000000
χ754-4-44-4-444-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-44-444-444-44-4-4000000000000000000000000000000000000000000000000000000000000
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).