Finite Group Databasebeta

← Group #360621

Character table — Group #360621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222222222222244444444444444444444444444448888888888888888444444444444444444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ1711111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−ii−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−i
χ1811111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111i−ii−i11-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−ii−ii
χ1911111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii11-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii
χ2011111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111−ii−ii11-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−ii−ii−i
χ2111111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−ii−i-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ2211111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111-1-1-1-11111i−ii−i-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iiii−ii−i
χ2311111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iiii−ii−i
χ2411111-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111-1-1-1-11111−ii−ii-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−ii−ii
χ2511111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-1111111-1-1-1-1ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111i−i−ii-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiii−i−ii
χ2611111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-1111111-1-1-1-1ii−i−i−i−iii-1-1-1-111111111-1-1-1-1i−i−ii-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−iii−i
χ2711111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-1111111-1-1-1-1−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−iii−i-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−iii−i
χ2811111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-1111111-1-1-1-1−i−iiiii−i−i-1-1-1-111111111-1-1-1-1−iii−i-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iiii−i−ii
χ2911111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111i−i−ii11-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−iii−i
χ3011111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1i−i−ii11-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−ii−i−ii
χ3111111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−iii−i11-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−ii−i−ii
χ3211111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1−iii−i11-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−iii−i
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222220000000000000000-2-2-2-200000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000222200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-20000000000000000-2-22200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-22222000000000000000022-2-200000000000000000000000000000000
χ3722222-2-2-2-2-2-2222-2-22222-2-2-2-2-2-2-22222-2-2-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i00000000000000000000000000000000
χ3822222-2-2-2-2-2-2222-2-22222-2-2-2-2-2-2-22222-2-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i00000000000000000000000000000000
χ3922222-2-2-2-2-2-2222-2-2-2-2-2-22222-2-2-22222-222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000000000000000000000000000
χ4022222-2-2-2-2-2-2222-2-2-2-2-2-22222-2-2-22222-222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000000000000000000000000000
χ41222-2-222-2-22-22-2-22-2000000002-2-22-22-2200002i2i−2i−2i2i2i−2i−2i000000000000000022-2-222-2-20000000000002i−2i2i−2i00000000000000000000
χ42222-2-222-2-22-22-2-22-2000000002-2-22-22-2200002i2i−2i−2i2i2i−2i−2i0000000000000000-2-222-2-222000000000000−2i2i−2i2i00000000000000000000
χ43222-2-222-2-22-22-2-22-2000000002-2-22-22-220000−2i−2i2i2i−2i−2i2i2i000000000000000022-2-222-2-2000000000000−2i2i−2i2i00000000000000000000
χ44222-2-222-2-22-22-2-22-2000000002-2-22-22-220000−2i−2i2i2i−2i−2i2i2i0000000000000000-2-222-2-2220000000000002i−2i2i−2i00000000000000000000
χ45222-2-2-2-222-222-2-2-22000000002-2-2-22-22200002i2i−2i−2i−2i−2i2i2i000000000000000022-2-2-2-2220000000000002i−2i−2i2i00000000000000000000
χ46222-2-2-2-222-222-2-2-22000000002-2-2-22-22200002i2i−2i−2i−2i−2i2i2i0000000000000000-2-22222-2-2000000000000−2i2i2i−2i00000000000000000000
χ47222-2-2-2-222-222-2-2-22000000002-2-2-22-2220000−2i−2i2i2i2i2i−2i−2i000000000000000022-2-2-2-222000000000000−2i2i2i−2i00000000000000000000
χ48222-2-2-2-222-222-2-2-22000000002-2-2-22-2220000−2i−2i2i2i2i2i−2i−2i0000000000000000-2-22222-2-20000000000002i−2i−2i2i00000000000000000000
χ4922-2-2-22-22-222-222-2-222-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i22−2−222−2−22−22−22−22−2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ5022-2-2-22-22-222-222-2-222-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i−2−222−2−222−22−22−22−22000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ5122-2-2-22-22-222-222-2-222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i22−2−222−2−22−22−22−22−2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ5222-2-2-22-22-222-222-2-222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i−2−222−2−222−22−22−22−22000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ5322-2-2-22-22-222-222-2-2-2-222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i22−2−222−2−2−22−22−22−22000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ5422-2-2-22-22-222-222-2-2-2-222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i−2−222−2−2222−22−22−22−2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ5522-2-2-22-22-222-222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i22−2−222−2−2−22−22−22−22000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ5622-2-2-22-22-222-222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i−2−222−2−2222−22−22−22−2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ5722-2-2-2-22-22-2-2-2222222-2-2-2-222000000000000000000002-2-222-2-2222−2−2−2−2222−22−2−22−220000000000000000000000002−2−222−2−220000
χ5822-2-2-2-22-22-2-2-2222222-2-2-2-222000000000000000000002-2-222-2-22−2−22222−2−2−22−222−22−2000000000000000000000000−222−2−222−20000
χ5922-2-2-2-22-22-2-2-2222222-2-2-2-22200000000000000000000-222-2-222-222−2−2−2−2222−22−2−22−22000000000000000000000000−222−2−222−20000
χ6022-2-2-2-22-22-2-2-2222222-2-2-2-22200000000000000000000-222-2-222-2−2−22222−2−2−22−222−22−20000000000000000000000002−2−222−2−220000
χ6122-2-2-2-22-22-2-2-22222-2-22222-2-2000000000000000000002-2-22-222-222−2−2−2−222−22−222−22−20000000000000000000000002−2−22−222−20000
χ6222-2-2-2-22-22-2-2-22222-2-22222-2-2000000000000000000002-2-22-222-2−2−22222−2−22−22−2−22−22000000000000000000000000−222−22−2−220000
χ6322-2-2-2-22-22-2-2-22222-2-22222-2-200000000000000000000-222-22-2-2222−2−2−2−222−22−222−22−2000000000000000000000000−222−22−2−220000
χ6422-2-2-2-22-22-2-2-22222-2-22222-2-200000000000000000000-222-22-2-22−2−22222−2−22−22−2−22−220000000000000000000000002−2−22−222−20000
χ652-2-22-22222-2-222-2-2-22-22-22-22-222-222-2-2-22-22-22-22-22-22-200000000000000000000000000002-22-20000000000000000000000000000
χ662-2-22-22222-2-222-2-2-22-22-22-22-222-222-2-2-22-22-2-22-22-22-220000000000000000000000000000-22-220000000000000000000000000000
χ672-2-22-22222-2-222-2-2-22-22-22-22-2-2-22-2-2222-22-220000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ682-2-22-22222-2-222-2-2-22-22-22-22-2-2-22-2-2222-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ692-2-22-22222-2-222-2-2-2-22-22-22-2222-222-2-2-2-22-222-22-22-22-20000000000000000000000000000-22-220000000000000000000000000000
χ702-2-22-22222-2-222-2-2-2-22-22-22-2222-222-2-2-2-22-22-22-22-22-2200000000000000000000000000002-22-20000000000000000000000000000
χ712-2-22-22222-2-222-2-2-2-22-22-22-22-2-22-2-22222-22-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ722-2-22-22222-2-222-2-2-2-22-22-22-22-2-22-2-22222-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ732-2-22-2-2-2-2-22222-2222-22-2-22-2222-2-2-222-22-2-222-22-2-22-2200000000000000000000000000002-2-220000000000000000000000000000
χ742-2-22-2-2-2-2-22222-2222-22-2-22-2222-2-2-222-22-2-22-22-222-22-20000000000000000000000000000-222-20000000000000000000000000000
χ752-2-22-2-2-2-2-22222-2222-22-2-22-22-2-2222-2-22-222-20000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ762-2-22-2-2-2-2-22222-2222-22-2-22-22-2-2222-2-22-222-2000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ772-2-22-2-2-2-2-22222-222-22-222-22-222-2-2-222-2-222-22-22-2-22-220000000000000000000000000000-222-20000000000000000000000000000
χ782-2-22-2-2-2-2-22222-222-22-222-22-222-2-2-222-2-222-2-22-222-22-200000000000000000000000000002-2-220000000000000000000000000000
χ792-2-22-2-2-2-2-22222-222-22-222-22-2-2-2222-2-222-2-220000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ802-2-22-2-2-2-2-22222-222-22-222-22-2-2-2222-2-222-2-22000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ812-2-2-2222-2-2-222-22-22000000002-222-2-22-200002i−2i−2i2i2i−2i−2i2i000000002i−2i2i−2i2i−2i2i−2i00000000000000002-22-2000000000000000000000000
χ822-2-2-2222-2-2-222-22-22000000002-222-2-22-200002i−2i−2i2i2i−2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000-22-22000000000000000000000000
χ832-2-2-2222-2-2-222-22-22000000002-222-2-22-20000−2i2i2i−2i−2i2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000-22-22000000000000000000000000
χ842-2-2-2222-2-2-222-22-22000000002-222-2-22-20000−2i2i2i−2i−2i2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000002-22-2000000000000000000000000
χ852-2-2-22-2-2222-22-222-2000000002-22-222-2-200002i−2i−2i2i−2i2i2i−2i000000002i−2i2i−2i−2i2i−2i2i00000000000000002-2-22000000000000000000000000
χ862-2-2-22-2-2222-22-222-2000000002-22-222-2-200002i−2i−2i2i−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000-222-2000000000000000000000000
χ872-2-2-22-2-2222-22-222-2000000002-22-222-2-20000−2i2i2i−2i2i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000-222-2000000000000000000000000
χ882-2-2-22-2-2222-22-222-2000000002-22-222-2-20000−2i2i2i−2i2i−2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000002-2-22000000000000000000000000
χ89444-4-444-4-44-44-4-44-400000000-444-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-4-444-444-4-4-4400000000-4444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4444-4-444-4-4-4-4-440000000000000000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ9244-4444-4-444-4-4-4-4-4400000000000000000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ9344-444-444-4-44-4-4-44-40000000000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ9444-444-444-4-44-4-4-44-400000000000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ954-444-44-4-44-44-4-444-40000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ964-444-44-4-44-44-4-444-4000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ974-444-4-444-44-4-4-44-440000000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ984-444-4-444-44-4-4-44-44000000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ994-44-444-44-4-4-4-44-4444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-444-44-4-4-4-44-444-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-4444-44-4-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-4444-44-4-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4444-4-4-444-44-4400000000-44-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-44-4-4444-44-444-400000000-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000

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