Finite Group Databasebeta

← Group #231559

Character table — Group #231559

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888822224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ17111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ18111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−i−i−iii−i−iii111-1-111-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ19111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1-1−i−iii−i−iiiii−i−iii−i−i111-1-111-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ20111-1-1-1-11-11111-1-1-11111-1-1-1-11111-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ21111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−iii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−ii−ii−i−ii−i−iii−i−iiiii−i−i−i−iii1-1-111-1-11
χ22111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−i−i−iiiii−i−i111-1-1-1-111-1-1-1-11111i−ii−i−iii−i−i−iii−i−iii−i−iiiii−i−i-111-1-111-1
χ23111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111-1−i−iii−i−iiiii−i−i−i−iii111-1-1-1-111-1-1-1-11111−ii−iii−i−iiii−i−iii−i−iii−i−i−i−iii-111-1-111-1
χ24111-1-1-1-11-11111-1-1-11111-1-1-1-1-1-1-1-11111-1−i−iii−i−iii−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−ii−ii−iii−iii−i−iii−i−i−i−iiiii−i−i1-1-111-1-11
χ25111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1-1ii−i−i−i−iiiii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−i−iii−ii−iii−i−i−i−iii−i−iii−i−iii1-1-11-111-1
χ26111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1-1ii−i−i−i−iii−i−iii−i−iii1-1-11111-1-1-1-1-1-11111i−i−ii−ii−iiii−i−i−i−iiiii−i−iii−i−i-111-11-1-11
χ27111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1-1−i−iiiii−i−iii−i−iii−i−i1-1-11111-1-1-1-1-1-11111−iii−ii−ii−i−i−iiiii−i−i−i−iii−i−iii-111-11-1-11
χ28111-1-1-1-11-11111-1-1-1-1-1-1-111111111-1-1-1-1-1−i−iiiii−i−i−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−iii−i−ii−ii−i−iiiii−i−iii−i−iii−i−i1-1-11-111-1
χ29111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−iii−i−ii−i−iiiii−i−i−i−iiiii−i−i1-11-1-11-11
χ30111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−i−i−iii−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1i−i−ii−iii−i−i−iiiii−i−iii−i−i−i−iii-11-111-11-1
χ31111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−iii−i−i−i−iii1-1-111-1-1111111-1-1-1-1−iii−ii−i−iiii−i−i−i−iii−i−iiiii−i−i-11-111-11-1
χ32111-1-1-1-11-11111-1-1-1-1-1-1-11111-1-1-1-11111-1−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−i−iii−iii−i−i−i−iiiii−i−i−i−iii1-11-1-11-11
χ33222222222-2-222-2-222222222200000000-22222222200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ34222222222-2-222-2-222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ35222222222-2-222-2-22-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-22222000000000000-2-2220000000000000000000000000000
χ36222222222-2-222-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-2222200000000000022-2-20000000000000000000000000000
χ3722222222-222-2-222-20000000022222222-20000000022222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ3822222222-222-2-222-20000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ3922222222-222-2-222-200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ4022222222-222-2-222-200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
χ41222-2-2-2-22222-2-2-2-22000000002222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ42222-2-2-2-22222-2-2-2-22000000002222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ43222-2-2-2-22222-2-2-2-2200000000-2-2-2-222222000000002i2i−2i−2i−2i−2i2i2i-2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ44222-2-2-2-22222-2-2-2-2200000000-2-2-2-22222200000000−2i−2i2i2i2i2i−2i−2i-2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ45222-2-2-2-22-2-2-22222-22222-2-2-2-20000000022i2i−2i−2i2i2i−2i−2i00000000-2-2-222000000000000−2i2i−2i2i0000000000000000000000000000
χ46222-2-2-2-22-2-2-22222-22222-2-2-2-2000000002−2i−2i2i2i−2i−2i2i2i00000000-2-2-2220000000000002i−2i2i−2i0000000000000000000000000000
χ47222-2-2-2-22-2-2-22222-2-2-2-2-222220000000022i2i−2i−2i−2i−2i2i2i00000000-222-2-2000000000000−2i2i2i−2i0000000000000000000000000000
χ48222-2-2-2-22-2-2-22222-2-2-2-2-22222000000002−2i−2i2i2i2i2i−2i−2i00000000-222-2-20000000000002i−2i−2i2i0000000000000000000000000000
χ4922-22-22-2-202-2002-20i2i2−i2−i2i2i2−i2−i22i2i−2i−2i2i2i−2i−2i0000000002-22-22i−2i2i−2i0i2−i2i2−i2000022−2−222−2−20000000000000000i2−i2i2−i22−22−200000000
χ5022-22-22-2-202-2002-20i2i2−i2−i2i2i2−i2−i22i2i−2i−2i2i2i−2i−2i000000000-22-22−2i2i−2i2i0i2−i2i2−i2000022−2−222−2−20000000000000000−i2i2−i2i2−22−2200000000
χ5122-22-22-2-202-2002-20i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i−2i−2i2i2i0000000002-22-2−2i2i−2i2i0i2−i2i2−i20000−2−222−2−2220000000000000000i2−i2i2−i2−22−2200000000
χ5222-22-22-2-202-2002-20i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i−2i−2i2i2i000000000-22-222i−2i2i−2i0i2−i2i2−i20000−2−222−2−2220000000000000000−i2i2−i2i22−22−200000000
χ5322-22-22-2-202-2002-20−i2−i2i2i2−i2−i2i2i22i2i−2i−2i2i2i−2i−2i0000000002-22-22i−2i2i−2i0−i2i2−i2i20000−2−222−2−2220000000000000000−i2i2−i2i2−22−2200000000
χ5422-22-22-2-202-2002-20−i2−i2i2i2−i2−i2i2i22i2i−2i−2i2i2i−2i−2i000000000-22-22−2i2i−2i2i0−i2i2−i2i20000−2−222−2−2220000000000000000i2−i2i2−i22−22−200000000
χ5522-22-22-2-202-2002-20−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i−2i−2i2i2i0000000002-22-2−2i2i−2i2i0−i2i2−i2i2000022−2−222−2−20000000000000000−i2i2−i2i22−22−200000000
χ5622-22-22-2-202-2002-20−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i−2i−2i2i2i000000000-22-222i−2i2i−2i0−i2i2−i2i2000022−2−222−2−20000000000000000i2−i2i2−i2−22−2200000000
χ5722-2-22-22-202-200-220i2i2−i2−i2−i2−i2i2i22i2i−2i−2i−2i−2i2i2i0000000002i−2i−2i2i-222-20i2−i2−i2i2000022−2−2−2−2220000000000000000−222−2i2−i2−i2i200000000
χ5822-2-22-22-202-200-220i2i2−i2−i2−i2−i2i2i22i2i−2i−2i−2i−2i2i2i000000000−2i2i2i−2i2-2-220i2−i2−i2i2000022−2−2−2−22200000000000000002−2−22−i2i2i2−i200000000
χ5922-2-22-22-202-200-220i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i2i2i−2i−2i0000000002i−2i−2i2i2-2-220i2−i2−i2i20000−2−22222−2−20000000000000000−222−2−i2i2i2−i200000000
χ6022-2-22-22-202-200-220i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i2i2i−2i−2i000000000−2i2i2i−2i-222-20i2−i2−i2i20000−2−22222−2−200000000000000002−2−22i2−i2−i2i200000000
χ6122-2-22-22-202-200-220−i2−i2i2i2i2i2−i2−i22i2i−2i−2i−2i−2i2i2i0000000002i−2i−2i2i-222-20−i2i2i2−i20000−2−22222−2−200000000000000002−2−22−i2i2i2−i200000000
χ6222-2-22-22-202-200-220−i2−i2i2i2i2i2−i2−i22i2i−2i−2i−2i−2i2i2i000000000−2i2i2i−2i2-2-220−i2i2i2−i20000−2−22222−2−20000000000000000−222−2i2−i2−i2i200000000
χ6322-2-22-22-202-200-220−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i2i2i−2i−2i0000000002i−2i−2i2i2-2-220−i2i2i2−i2000022−2−2−2−22200000000000000002−2−22i2−i2−i2i200000000
χ6422-2-22-22-202-200-220−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i2i2i−2i−2i000000000−2i2i2i−2i-222-20−i2i2i2−i2000022−2−2−2−2220000000000000000−222−2−i2i2i2−i200000000
χ652-2-222-2-222002-200-22-22-22-22-22−22−22−22−202i−2i2i−2i2i−2i2i−2i00000000000002−22−22−22−22−22−200000000i2−i2i2−i2i2−i2i2−i20000000000000000
χ662-2-222-2-222002-200-22-22-22-22-22−22−22−22−20−2i2i−2i2i−2i2i−2i2i00000000000002−22−22−22−22−22−200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ672-2-222-2-222002-200-22-22-22-22-2−22−22−22−2202i−2i2i−2i2i−2i2i−2i0000000000000−22−22−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ682-2-222-2-222002-200-22-22-22-22-2−22−22−22−220−2i2i−2i2i−2i2i−2i2i0000000000000−22−22−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i20000000000000000
χ692-2-222-2-222002-200-2-22-22-22-222−22−22−22−202i−2i2i−2i−2i2i−2i2i00000000000002−22−2−22−22−22−2200000000i2−i2i2−i2−i2i2−i2i20000000000000000
χ702-2-222-2-222002-200-2-22-22-22-222−22−22−22−20−2i2i−2i2i2i−2i2i−2i00000000000002−22−2−22−22−22−2200000000−i2i2−i2i2i2−i2i2−i20000000000000000
χ712-2-222-2-222002-200-2-22-22-22-22−22−22−22−2202i−2i2i−2i−2i2i−2i2i0000000000000−22−222−22−22−22−200000000−i2i2−i2i2i2−i2i2−i20000000000000000
χ722-2-222-2-222002-200-2-22-22-22-22−22−22−22−220−2i2i−2i2i2i−2i2i−2i0000000000000−22−222−22−22−22−200000000i2−i2i2−i2−i2i2−i2i20000000000000000
χ732-2-2-2-2222-2002-20022-22-2-22-222−22−2−22−2202-2-222-2-2200000000000002−2−222−22−2−22−22000000002−2−222−2−220000000000000000
χ742-2-2-2-2222-2002-20022-22-2-22-222−22−2−22−220-222-2-222-200000000000002−2−222−22−2−22−2200000000−222−2−222−20000000000000000
χ752-2-2-2-2222-2002-20022-22-2-22-22−22−222−22−202-2-222-2-220000000000000−222−2−22−222−22−200000000−222−2−222−20000000000000000
χ762-2-2-2-2222-2002-20022-22-2-22-22−22−222−22−20-222-2-222-20000000000000−222−2−22−222−22−2000000002−2−222−2−220000000000000000
χ772-2-2-2-2222-2002-2002-22-222-22-22−22−2−22−2202-2-22-222-200000000000002−2−22−22−222−22−2000000002−2−22−222−20000000000000000
χ782-2-2-2-2222-2002-2002-22-222-22-22−22−2−22−220-222-22-2-2200000000000002−2−22−22−222−22−200000000−222−22−2−220000000000000000
χ792-2-2-2-2222-2002-2002-22-222-22-2−22−222−22−202-2-22-222-20000000000000−222−22−22−2−22−2200000000−222−22−2−220000000000000000
χ802-2-2-2-2222-2002-2002-22-222-22-2−22−222−22−20-222-22-2-220000000000000−222−22−22−2−22−22000000002−2−22−222−20000000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
χ82444-4-4-4-444-4-4-4-44440000000000000000-400000000000000004000000000000000000000000000000000000000000000000
χ8344-44-44-4-40-4400-4402i22i2−2i2−2i22i22i2−2i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8444-44-44-4-40-4400-440−2i2−2i22i22i2−2i2−2i22i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ8544-4-44-44-40-44004-402i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ8644-4-44-44-40-44004-40−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ874-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ884-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ894-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ904-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ914-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ924-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ934-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ944-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ954-4-444-4-44-400-440040000000022−2222−2222−2222−220000000000000000000000−2222−22220000000000000000000000000000000000000000
χ964-4-444-4-44-400-4400400000000−2222−2222−2222−2222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ974-4-4-4-4444400-4400-40000000022−2222−22−2222−22220000000000000000000000−222222−220000000000000000000000000000000000000000
χ984-4-4-4-4444400-4400-400000000−2222−222222−2222−22000000000000000000000022−22−22220000000000000000000000000000000000000000

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