Finite Group Databasebeta

← Group #494813

Character table — Group #494813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order122222222244444444888888888888888888444444444444888888881616161616161616161616161616161644444444
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-1111-1-11-1-111111-1-1-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ10111111-1-1-1-1111-1-11-1-111111-1-1-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ11111111-1-1-1-1111-1-11-1-111111-1-1-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ12111111-1-1-1-1111-1-11-1-111111-1-1-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ13111111-1-1-1-1111-1-11-1-111111-1-1-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ14111111-1-1-1-1111-1-11-1-111111-1-1-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ15111111-1-1-1-1111-1-11-1-111111-1-1-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ16111111-1-1-1-1111-1-11-1-111111-1-1-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ171111-1-111-1-11-1-1111-1-1-1-1-1-1111-1ii−i−iii−i−i1-111-1-111-1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181111-1-111-1-11-1-1111-1-1-1-1-1-1111-1ii−i−iii−i−i1-111-1-111-1-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191111-1-111-1-11-1-1111-1-1-1-1-1-1111-1ii−i−iii−i−i1-1-1-111-1-111i−ii−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201111-1-111-1-11-1-1111-1-1-1-1-1-1111-1ii−i−iii−i−i1-1-1-111-1-111i−ii−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211111-1-111-1-11-1-1111-1-1-1-1-1-1111-1−i−iii−i−iii1-111-1-111-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ221111-1-111-1-11-1-1111-1-1-1-1-1-1111-1−i−iii−i−iii1-111-1-111-1-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ231111-1-111-1-11-1-1111-1-1-1-1-1-1111-1−i−iii−i−iii1-1-1-111-1-111−ii−iiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241111-1-111-1-11-1-1111-1-1-1-1-1-1111-1−i−iii−i−iii1-1-1-111-1-111−ii−iiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ261111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-1-111-1
χ271111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-11111-1-11111-1-11-1-11-1-11111-1-111-1-1-1-11111-1-1-1-111-111-1-111-1
χ281111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-11111-1-11111-1-11-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ291111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-11-1-11111-1-11111-1-1-1-111-111-1-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ301111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-11-1-11111-1-11111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ311111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-11-1-11111-1-111-1-11111-1-1-111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1-11
χ321111-1-1-1-1111-1-1-1-1111-1-1-1-11-1-11-1-11111-1-111-1-11111-1-1-111-111-1-1-1-111-1-11111-1-111-1-1-1-1111-1-11-111-1
χ33222222222222222222-2-2-2-2-2-2-2-222222222-2-200000000-2-2-2-200000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ35222222-2-2-2-2222-2-22-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i00000000000000000000000000000000
χ36222222-2-2-2-2222-2-22-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i00000000000000000000000000000000
χ372222-2-222-2-22-2-2222-2-22222-2-2-222i2i−2i−2i2i2i−2i−2i-2200000000−2i2i−2i2i00000000000000000000000000000000
χ382222-2-222-2-22-2-2222-2-22222-2-2-22−2i−2i2i2i−2i−2i2i2i-22000000002i−2i2i−2i00000000000000000000000000000000
χ392222-2-2-2-2222-2-2-2-22222222-222-222-2-2-2-222-2-200000000-222-200000000000000000000000000000000
χ402222-2-2-2-2222-2-2-2-22222222-222-2-2-22222-2-2-2-2000000002-2-2200000000000000000000000000000000
χ4122-2-22-22-22-222-22-2-22-2000000002-22-22-22-200000000000000000000002−22−22−22−22−22−22−22−200000000
χ4222-2-22-22-22-222-22-2-22-2000000002-22-22-22-20000000000000000000000−22−22−22−22−22−22−22−2200000000
χ4322-2-22-22-22-222-22-2-22-200000000-22-22-22-2200000000000000000000002−22−22−22−2−22−22−22−2200000000
χ4422-2-22-22-22-222-22-2-22-200000000-22-22-22-220000000000000000000000−22−22−22−222−22−22−22−200000000
χ4522-2-22-22-22-2-2-22-222-2222-2-222-2200000000-2-20000000000002-22-22-22-2000000000000000000000000
χ4622-2-22-22-22-2-2-22-222-2222-2-222-2200000000-2-2000000000000-22-22-22-22000000000000000000000000
χ4722-2-22-22-22-2-2-22-222-22-2-222-2-22-200000000222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ4822-2-22-22-22-2-2-22-222-22-2-222-2-22-20000000022−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ4922-2-22-2-22-2222-2-22-2-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ5022-2-22-2-22-2222-2-22-2-22000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ5122-2-22-2-22-2222-2-22-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ5222-2-22-2-22-2222-2-22-2-2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ5322-2-22-2-22-22-2-222-222-222-2-22-22-200000000-220000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5422-2-22-2-22-22-2-222-222-222-2-22-22-200000000-22000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5522-2-22-2-22-22-2-222-222-2-2-222-22-22000000002-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ5622-2-22-2-22-22-2-222-222-2-2-222-22-22000000002-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ5722-2-2-222-2-222-222-2-2-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ5822-2-2-222-2-222-222-2-2-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ5922-2-2-222-2-222-222-2-2-2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ6022-2-2-222-2-222-222-2-2-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ6122-2-2-222-2-22-22-2-2222-222-2-2-2-222000000002-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ6222-2-2-222-2-22-22-2-2222-222-2-2-2-222000000002-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ6322-2-2-222-2-22-22-2-2222-2-2-22222-2-200000000-220000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ6422-2-2-222-2-22-22-2-2222-2-2-22222-2-200000000-22000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ6522-2-2-22-222-22-22-22-22-2000000002-2-22-222-200000000000000000000002−2−22−222−22−2−22−222−200000000
χ6622-2-2-22-222-22-22-22-22-2000000002-2-22-222-20000000000000000000000−222−22−2−22−222−22−2−2200000000
χ6722-2-2-22-222-22-22-22-22-200000000-222-22-2-2200000000000000000000002−2−22−222−2−222−22−2−2200000000
χ6822-2-2-22-222-22-22-22-22-200000000-222-22-2-220000000000000000000000−222−22−2−222−2−22−222−200000000
χ6922-2-2-22-222-2-22-22-22-2222-2-2-22-2-200000000222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ7022-2-2-22-222-2-22-22-22-2222-2-2-22-2-20000000022−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ7122-2-2-22-222-2-22-22-22-22-2-2222-22200000000-2-20000000000002-2-22-222-2000000000000000000000000
χ7222-2-2-22-222-2-22-22-22-22-2-2222-22200000000-2-2000000000000-222-22-2-22000000000000000000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-4-4-444-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ778-88-80000000000000042−4242−420000000000000000000000000000000000000000000000000000000000
χ788-88-800000000000000−4242−42420000000000000000000000000000000000000000000000000000000000
χ798-8-880000000000000042−42−42420000000000000000000000000000000000000000000000000000000000
χ808-8-8800000000000000−424242−420000000000000000000000000000000000000000000000000000000000

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