Finite Group Databasebeta

← Group #368484

Character table — Group #368484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444444444444444444444448888888888888888444444444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ171111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-11-111-1-1i−iii−i−iii−i−iii−i−i11-1-1i−i1-1
χ181111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−i1111-1-1-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-1111-111-1-1i−iii−i−iii−i−i−i−iii-1-111−ii-11
χ191111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−i-1-1-1-11111ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-1111-1-1-111i−i−i−iii−i−iiiii−i−i11-1-1−ii-11
χ201111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-11-1-1-111i−i−i−iii−i−iii−i−iii-1-111i−i1-1
χ211111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-1-1-111−i−iii1111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1-11-1-111−iiii−i−i−i−iii−i−iii-1-111−ii-11
χ221111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-1-1-111−i−iii1111-1-1-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-111-11-1-111−iiii−i−i−i−iiiii−i−i11-1-1i−i1-1
χ231111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-1-1-11111ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-1111-1-1−ii−i−iiiii−i−i−i−iii-1-111i−i1-1
χ241111-1-1-1-111-1-1-111-1iiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1-1111-1-1−ii−i−iiiii−i−iii−i−i11-1-1−ii-11
χ251111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii1111-1-1-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-1111-111-1-1−ii−i−iii−i−iiiii−i−i-1-111i−i-11
χ261111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-11-111-1-1−ii−i−iii−i−iii−i−iii11-1-1−ii1-1
χ271111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-11-1-1-111−iiii−i−iii−i−iii−i−i-1-111−ii1-1
χ281111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii-1-1-1-11111−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-1111-1-1-111−iiii−i−iii−i−i−i−iii11-1-1i−i-11
χ291111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i1111-1-1-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-111-11-1-111i−i−i−iiiii−i−i−i−iii11-1-1−ii1-1
χ301111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i1111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1-11-1-111i−i−i−iiiii−i−iii−i−i-1-111i−i-11
χ311111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-1-1111-1-1i−iii−i−i−i−iii−i−iii11-1-1i−i-11
χ321111-1-1-1-111-1-1-111-1−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-1-1-11111−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-1111-1-1i−iii−i−i−i−iiiii−i−i-1-111−ii1-1
χ33222222222222222222222222-2-2-2-2-2-2-2-22222222200000000-2-2-2-2000000000000000000000000-2-20000-2-200000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000002200002200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000002222000000000000000000000000-2-200002200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222000000000000000000000000220000-2-200000000000000000000
χ372222-2-2-2-222-2-2-222-22i2i2i2i−2i−2i−2i−2i-2-222-2-22222-2-22i2i−2i−2i00000000−2i−2i2i2i000000000000000000000000-220000−2i2i00000000000000000000
χ382222-2-2-2-222-2-2-222-22i2i2i2i−2i−2i−2i−2i-2-222-2-222-2-222−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000002-200002i−2i00000000000000000000
χ392222-2-2-2-222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-2-222-2-22222-2-2−2i−2i2i2i000000002i2i−2i−2i000000000000000000000000-2200002i−2i00000000000000000000
χ402222-2-2-2-222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-2-222-2-222-2-2222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000002-20000−2i2i00000000000000000000
χ41222-2222-22-22-2-2-2-2-222-2-222-2-2000000002-22-22-22-200000000000022−2−222−2−222−2−222−2−20000000000000000000000002−22−22−22−20000
χ42222-2222-22-22-2-2-2-2-222-2-222-2-2000000002-22-22-22-2000000000000−2−222−2−222−2−222−2−222000000000000000000000000−22−22−22−220000
χ43222-2222-22-22-2-2-2-2-222-2-222-2-200000000-22-22-22-2200000000000022−2−222−2−222−2−222−2−2000000000000000000000000−22−22−22−220000
χ44222-2222-22-22-2-2-2-2-222-2-222-2-200000000-22-22-22-22000000000000−2−222−2−222−2−222−2−2220000000000000000000000002−22−22−22−20000
χ45222-2222-22-22-2-2-2-2-2-2-222-2-222000000002-22-2-22-2200000000000022−2−222−2−2−2−222−2−2220000000000000000000000002−22−2−22−220000
χ46222-2222-22-22-2-2-2-2-2-2-222-2-222000000002-22-2-22-22000000000000−2−222−2−22222−2−222−2−2000000000000000000000000−22−222−22−20000
χ47222-2222-22-22-2-2-2-2-2-2-222-2-22200000000-22-222-22-200000000000022−2−222−2−2−2−222−2−222000000000000000000000000−22−222−22−20000
χ48222-2222-22-22-2-2-2-2-2-2-222-2-22200000000-22-222-22-2000000000000−2−222−2−22222−2−222−2−20000000000000000000000002−22−2−22−220000
χ49222-2-2-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i000000002-2-222i−2i−2i2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000000000i2−i2−i2i22−2−220000
χ50222-2-2-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i000000002-2-222i−2i−2i2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000000000−i2i2i2−i2−222−20000
χ51222-2-2-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i00000000-222-2−2i2i2i−2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000000000−i2i2i2−i2−222−20000
χ52222-2-2-2-222-2-222-2-222i2i−2i−2i−2i−2i2i2i00000000-222-2−2i2i2i−2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000000000i2−i2−i2i22−2−220000
χ53222-2-2-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000002-2-22−2i2i2i−2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000000000i2−i2−i2i2−222−20000
χ54222-2-2-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000002-2-22−2i2i2i−2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000000000−i2i2i2−i22−2−220000
χ55222-2-2-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i00000000-222-22i−2i−2i2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000000000−i2i2i2−i22−2−220000
χ56222-2-2-2-222-2-222-2-22−2i−2i2i2i2i2i−2i−2i00000000-222-22i−2i−2i2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000000000i2−i2−i2i2−222−20000
χ5722-2222-2-2-2-2-222-22-2000000002-2-2-22-2220000000022-2-222-2-20000000000002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i0000000000000000000000000000
χ5822-2222-2-2-2-2-222-22-2000000002-2-2-22-2220000000022-2-222-2-2000000000000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000000000
χ5922-2222-2-2-2-2-222-22-2000000002-2-2-22-22200000000-2-222-2-2220000000000002i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i0000000000000000000000000000
χ6022-2222-2-2-2-2-222-22-2000000002-2-2-22-22200000000-2-222-2-222000000000000−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i0000000000000000000000000000
χ6122-22-2-222-2-22-2-2-222000000002-2222-2-2-20000000022-2-2-2-2220000000000002i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i0000000000000000000000000000
χ6222-22-2-222-2-22-2-2-222000000002-2222-2-2-20000000022-2-2-2-222000000000000−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i0000000000000000000000000000
χ6322-22-2-222-2-22-2-2-222000000002-2222-2-2-200000000-2-22222-2-20000000000002i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i0000000000000000000000000000
χ6422-22-2-222-2-22-2-2-222000000002-2222-2-2-200000000-2-22222-2-2000000000000−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i0000000000000000000000000000
χ652-22-22-222-22-22-2-22-200000000-2-22-2222-2000000002-22-22-22-200002i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i00000000000000000000000000000000
χ662-22-22-222-22-22-2-22-200000000-2-22-2222-2000000002-22-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000000000000000
χ672-22-22-222-22-22-2-22-200000000-2-22-2222-200000000-22-22-22-2200002i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i00000000000000000000000000000000
χ682-22-22-222-22-22-2-22-200000000-2-22-2222-200000000-22-22-22-220000−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i00000000000000000000000000000000
χ692-22-2-22-2-2-222-22-22200000000-2-2-2222-22000000002-22-2-22-2200002-22-2-22-22000000002-2-2200000000000000000000000000000000
χ702-22-2-22-2-2-222-22-22200000000-2-2-2222-22000000002-22-2-22-220000-22-222-22-200000000-222-200000000000000000000000000000000
χ712-22-2-22-2-2-222-22-22200000000-2-2-2222-2200000000-22-222-22-200002-22-2-22-2200000000-222-200000000000000000000000000000000
χ722-22-2-22-2-2-222-22-22200000000-2-2-2222-2200000000-22-222-22-20000-22-222-22-2000000002-2-2200000000000000000000000000000000
χ732-2-2-22-2-2-22-222-22222-22-22-22-22-22-2-22-2200000000000000002-22-2000000000000000000000000002-22-20000002-22-2000000000000
χ742-2-2-22-2-2-22-222-22222-22-22-22-22-22-2-22-2200000000000000002-22-200000000000000000000000000-22-22000000-22-22000000000000
χ752-2-2-22-2-2-22-222-22222-22-22-22-2-22-222-22-2000000002-2-222-2-22-22-22000000000000000000000000000000002-22-20000000000000000
χ762-2-2-22-2-2-22-222-22222-22-22-22-2-22-222-22-200000000-222-2-222-2-22-2200000000000000000000000000000000-22-220000000000000000
χ772-2-2-22-2-2-22-222-2222-22-22-22-222-22-2-22-220000000000000000-22-22000000000000000000000000002-22-2000000-22-22000000000000
χ782-2-2-22-2-2-22-222-2222-22-22-22-222-22-2-22-220000000000000000-22-2200000000000000000000000000-22-220000002-22-2000000000000
χ792-2-2-22-2-2-22-222-2222-22-22-22-22-22-222-22-2000000002-2-222-2-222-22-200000000000000000000000000000000-22-220000000000000000
χ802-2-2-22-2-2-22-222-2222-22-22-22-22-22-222-22-200000000-222-2-222-22-22-2000000000000000000000000000000002-22-20000000000000000
χ812-2-2-2-22222-2-2-2222-22i−2i2i−2i−2i2i−2i2i2-2-22-222-200000000000000002i−2i−2i2i000000000000000000000000002-2-220000002i−2i−2i2i000000000000
χ822-2-2-2-22222-2-2-2222-22i−2i2i−2i−2i2i−2i2i2-2-22-222-200000000000000002i−2i−2i2i00000000000000000000000000-222-2000000−2i2i2i−2i000000000000
χ832-2-2-2-22222-2-2-2222-22i−2i2i−2i−2i2i−2i2i-222-22-2-22000000002-2-22-222-2−2i2i2i−2i000000000000000000000000000000002i−2i−2i2i0000000000000000
χ842-2-2-2-22222-2-2-2222-22i−2i2i−2i−2i2i−2i2i-222-22-2-2200000000-222-22-2-22−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i0000000000000000
χ852-2-2-2-22222-2-2-2222-2−2i2i−2i2i2i−2i2i−2i2-2-22-222-20000000000000000−2i2i2i−2i000000000000000000000000002-2-22000000−2i2i2i−2i000000000000
χ862-2-2-2-22222-2-2-2222-2−2i2i−2i2i2i−2i2i−2i2-2-22-222-20000000000000000−2i2i2i−2i00000000000000000000000000-222-20000002i−2i−2i2i000000000000
χ872-2-2-2-22222-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-222-22-2-22000000002-2-22-222-22i−2i−2i2i00000000000000000000000000000000−2i2i2i−2i0000000000000000
χ882-2-2-2-22222-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-222-22-2-2200000000-222-22-2-222i−2i−2i2i000000000000000000000000000000002i−2i−2i2i0000000000000000
χ8944-4444-4-4-4-4-444-44-400000000-4444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-444-4-44-4-4-44400000000-44-4-4-4444000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-44-44-4-4-44-44000000000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ9244-4-444-44-44-4-4-44-4400000000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ9344-4-4-4-44-4-444444-4-4000000000000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ9444-4-4-4-44-4-444444-4-400000000000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ954-4444-44-4-4-4-4-444-440000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ964-4444-44-4-4-4-4-444-44000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ974-444-44-44-4-444-44-4-400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ984-444-44-44-4-444-44-4-4000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ994-44-44-444-44-44-4-44-40000000044-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-44-4-4-444-44-44400000000444-4-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-444-4-44444-44-4-4-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-444-4-44444-44-4-4-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-444-44-4-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-444-44-4-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000

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