Finite Group Databasebeta

← Group #231558

Character table — Group #231558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888822224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ17111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1111-1-111-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ18111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-1111-1-111-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ19111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-1111-1-111-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ20111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ21111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−i−i−iii-1111-1-1-1-111-1-1-1-11111i−ii−ii−i−ii−i−iii−i−iiiii−i−i−i−iii1-1-111-1-11
χ22111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iiiii−i−i-1111-1-1-1-111-1-1-1-11111i−ii−i−iii−i−i−iii−i−iii−i−iiiii−i−i-111-1-111-1
χ23111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−i−i−iii-1111-1-1-1-111-1-1-1-11111−ii−iii−i−iiii−i−iii−i−iii−i−i−i−iii-111-1-111-1
χ24111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iiiii−i−i-1111-1-1-1-111-1-1-1-11111−ii−ii−iii−iii−i−iii−i−i−i−iiiii−i−i1-1-111-1-11
χ25111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−iii−i−i-11-1-11111-1-1-1-1-1-11111−iii−ii−ii−iii−i−i−i−iii−i−iii−i−iii-11-111-11-1
χ26111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iii−i−iii-11-1-11111-1-1-1-1-1-11111−iii−i−ii−iiii−i−i−i−iiiii−i−iii−i−i1-11-1-11-11
χ27111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−iii−i−i-11-1-11111-1-1-1-1-1-11111i−i−iii−ii−i−i−iiiii−i−i−i−iii−i−iii1-11-1-11-11
χ28111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii−i−iii-11-1-11111-1-1-1-1-1-11111i−i−ii−ii−ii−i−iiiii−i−iii−i−iii−i−i-11-111-11-1
χ29111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11-1-111-1-1111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ30111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-11-1-111-1-1111111-1-1-1-1−iii−i−iii−i−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ31111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-11-1-111-1-1111111-1-1-1-1i−i−iii−i−iiii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ32111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11-1-111-1-1111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ3322222222222-2-2-2-2222222222000000002222222200000000-2-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3422222222222-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000-2-2-2-2-2-200000000000022220000000000000000000000000000
χ3522222222222-2-2-2-22-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000-2-2222200000000000022-2-20000000000000000000000000000
χ3622222222222-2-2-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000-2-22222000000000000-2-2220000000000000000000000000000
χ3722222222-2-2-22222-200000000222222220000000022222222-2-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ3822222222-2-2-22222-2000000002222222200000000-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ3922222222-2-2-22222-200000000-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ4022222222-2-2-22222-200000000-2-2-2-2-2-2-2-200000000-2-2-2-22222-2-20000222200000000000022-2-2000000000000000000000000
χ41222-2-2-2-222-2-222-2-22000000002222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i2-20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ42222-2-2-2-222-2-222-2-22000000002222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i2-20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ43222-2-2-2-222-2-222-2-2200000000-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i2-2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ44222-2-2-2-222-2-222-2-2200000000-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i2-2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ45222-2-2-2-22-222-2-222-22222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000002-2-2-222000000000000−2i2i−2i2i0000000000000000000000000000
χ46222-2-2-2-22-222-2-222-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000002-2-2-2220000000000002i−2i2i−2i0000000000000000000000000000
χ47222-2-2-2-22-222-2-222-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000002-222-2-20000000000002i−2i−2i2i0000000000000000000000000000
χ48222-2-2-2-22-222-2-222-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000002-222-2-2000000000000−2i2i2i−2i0000000000000000000000000000
χ4922-222-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i22−2−222−2−22-22-22i−2i2i−2i000000000000002−22−2i2i2−i2−i2i2i2−i2−i2000000002−22−2i2−i2i2−i20000000000000000
χ5022-222-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-22−2i2i−2i2i000000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−22−22−i2i2−i2i20000000000000000
χ5122-222-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-22i−2i2i−2i00000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−22−22−i2i2−i2i20000000000000000
χ5222-222-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-22−2i2i−2i2i00000000000000−22−22−i2−i2i2i2−i2−i2i2i2000000002−22−2i2−i2i2−i20000000000000000
χ5322-222-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-2−2i2i−2i2i000000000000002−22−2−i2−i2i2i2−i2−i2i2i2000000002−22−2−i2i2−i2i20000000000000000
χ5422-222-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-222i−2i2i−2i000000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−22−22i2−i2i2−i20000000000000000
χ5522-222-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-2−2i2i−2i2i00000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−22−22i2−i2i2−i20000000000000000
χ5622-222-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i−2−222−2−222-22-222i−2i2i−2i00000000000000−22−22i2i2−i2−i2i2i2−i2−i2000000002−22−2−i2i2−i2i20000000000000000
χ5722-2-2-222-222-20000-22i2i−2i−2i−2i−2i2i2i22−2−2−2−2222i−2i−2i2i-222-2000000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2−222−20000000000000000
χ5822-2-2-222-222-20000-22i2i−2i−2i−2i−2i2i2i22−2−2−2−222−2i2i2i−2i2-2-22000000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i22−2−220000000000000000
χ5922-2-2-222-222-20000-22i2i−2i−2i−2i−2i2i2i−2−22222−2−22i−2i−2i2i-222-200000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i22−2−220000000000000000
χ6022-2-2-222-222-20000-22i2i−2i−2i−2i−2i2i2i−2−22222−2−2−2i2i2i−2i2-2-2200000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2−222−20000000000000000
χ6122-2-2-222-222-20000-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−2222i−2i−2i2i2-2-22000000000000002−2−22−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i22−2−220000000000000000
χ6222-2-2-222-222-20000-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−222−2i2i2i−2i-222-2000000000000002−2−22−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i2−222−20000000000000000
χ6322-2-2-222-222-20000-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−22i−2i−2i2i2-2-2200000000000000−222−2i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i2−222−20000000000000000
χ6422-2-2-222-222-20000-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−2−2i2i2i−2i-222-200000000000000−222−2i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i22−2−220000000000000000
χ652-222-22-2-20002-22-20i2−i2i2−i2i2−i2i2−i22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i00i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i200000000000000002−22−22−22−200000000
χ662-222-22-2-20002-22-20i2−i2i2−i2i2−i2i2−i22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i00i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000000000−22−22−22−2200000000
χ672-222-22-2-20002-22-20i2−i2i2−i2i2−i2i2−i2-22-22-22-22000000002i−2i2i−2i−2i2i−2i2i00i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i200000000000000002−22−2−22−2200000000
χ682-222-22-2-20002-22-20i2−i2i2−i2i2−i2i2−i2-22-22-22-2200000000−2i2i−2i2i2i−2i2i−2i00i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000000000000000−22−222−22−200000000
χ692-222-22-2-20002-22-20−i2i2−i2i2−i2i2−i2i22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i00−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000000000−22−22−22−2200000000
χ702-222-22-2-20002-22-20−i2i2−i2i2−i2i2−i2i22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i00−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i200000000000000002−22−22−22−200000000
χ712-222-22-2-20002-22-20−i2i2−i2i2−i2i2−i2i2-22-22-22-22000000002i−2i2i−2i−2i2i−2i2i00−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000000000−22−222−22−200000000
χ722-222-22-2-20002-22-20−i2i2−i2i2−i2i2−i2i2-22-22-22-2200000000−2i2i−2i2i2i−2i2i−2i00−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i200000000000000002−22−2−22−2200000000
χ732-22-22-22-20002-2-220i2−i2i2−i2−i2i2−i2i22-22-2-22-22000000002-2-222-2-2200i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ742-22-22-22-20002-2-220i2−i2i2−i2−i2i2−i2i22-22-2-22-2200000000-222-2-222-200i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ752-22-22-22-20002-2-220i2−i2i2−i2−i2i2−i2i2-22-222-22-2000000002-2-22-222-200i2−i2−i2i20000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ762-22-22-22-20002-2-220i2−i2i2−i2−i2i2−i2i2-22-222-22-200000000-222-22-2-2200i2−i2−i2i20000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ772-22-22-22-20002-2-220−i2i2−i2i2i2−i2i2−i22-22-2-22-22000000002-2-222-2-2200−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ782-22-22-22-20002-2-220−i2i2−i2i2i2−i2i2−i22-22-2-22-2200000000-222-2-222-200−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ792-22-22-22-20002-2-220−i2i2−i2i2i2−i2i2−i2-22-222-22-2000000002-2-22-222-200−i2i2i2−i20000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ802-22-22-22-20002-2-220−i2i2−i2i2i2−i2i2−i2-22-222-22-200000000-222-22-2-2200−i2i2i2−i20000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000000000000000000044000000000000000000000000000000000000000000000000
χ82444-4-4-4-444-4-4-4-444400000000000000000000000000000000-44000000000000000000000000000000000000000000000000
χ8344-444-4-4-44-440000-4000000002222−22−222222−22−220000000000000000000000−2222−22220000000000000000000000000000000000000000
χ8444-444-4-4-44-440000-400000000−22−222222−22−222222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ8544-4-4-444-4-4-4400004000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ8644-4-4-444-4-4-440000400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000
χ874-444-44-4-4000-44-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ884-444-44-4-4000-44-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ894-44-44-44-4000-444-402i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-44-44-44-4000-444-40−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-44-4-4440000000022−22−222222−22−222222−22−222222−22−2222000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ924-4-44-4-4440000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ934-4-44-4-44400000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ944-4-44-4-44400000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ954-4-4-444-440000000022−22−2222−222222−2222−22−2222−222222−22000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ964-4-4-444-440000000022−22−2222−222222−22−222222−2222−22−222200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ974-4-4-444-4400000000−222222−2222−22−222222−22−2222−222222−2200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ984-4-4-444-4400000000−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000002-2-22-222-200000000000000000000000000000000

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