Finite Group Databasebeta

← Group #12009308

Character table — Group #12009308

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111222222222222222222444444444444444444444488888888888888888888888888881010101016161616161616161616161616161616161620202020202040404040404040408080
order122244444455888810101010101088202020202020202020202020404040404040404088881616161640404040808080808080808080808080808080804444442020202020202020404040404040404024888888881616161644
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11-11111-1-1-1-1iiii−i−i−i−i-1111-1-1ii−i−iii−i−i1-1
χ101111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-1111-11111-1-1-1-1iiii−i−i−i−i1-1-1-111−i−iii−i−iii-11
χ111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11-1-1-1-11111iiii−i−i−i−i-1111-1-1ii−i−i−i−iii-11
χ121111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-11-1-1-1-11111iiii−i−i−i−i1-1-1-111−i−iiiii−i−i1-1
χ131111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11-1-1-1-11111−i−i−i−iiiii-1111-1-1−i−iiiii−i−i-11
χ141111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-11-1-1-1-11111−i−i−i−iiiii1-1-1-111ii−i−i−i−iii1-1
χ151111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11-11111-1-1-1-1−i−i−i−iiiii-1111-1-1−i−iii−i−iii1-1
χ161111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1111−i−i−i−i−i−i−i−iiiiiiiii-1-1111-11111-1-1-1-1−i−i−i−iiiii1-1-1-111ii−i−iii−i−i-11
χ17222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000222200000000000000000022-2-2-2-20000000000
χ18222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000-2-2-2-2000000000000000000-2-222220000000000
χ192222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ202222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+520000-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ212222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ222222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52000022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ232222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ242222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−520000-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ252222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ262222222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52000022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ27222222-2-2-2-2220000222222002222-2-2-2-2-2-2-2-2000000000000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222-2-20000000000000000002-200000000i2−i2i2−i200
χ28222222-2-2-2-2220000222222002222-2-2-2-2-2-2-2-2000000000000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2-222000000000000000000-2200000000−i2i2−i2i200
χ29222222-2-2-2-2220000222222002222-2-2-2-2-2-2-2-2000000000000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222-2-20000000000000000002-200000000−i2i2−i2i200
χ30222222-2-2-2-2220000222222002222-2-2-2-2-2-2-2-2000000000000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2-222000000000000000000-2200000000i2−i2i2−i200
χ312222-2-222-2-2222222222222-2-2-2-2-2-22222-2-2-2-22222222200000000-2-2-2-2000000000000000022-2-2000000000000000000-22-2-2220000000000
χ322222-2-222-2-2222222222222-2-2-2-2-2-22222-2-2-2-22222222200000000-2-2-2-20000000000000000-2-2220000000000000000002-222-2-20000000000
χ332222-2-222-2-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+522i2i−2i−2i2i2i−2i−2i−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ1400002-2−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
χ342222-2-222-2-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+522i2i−2i−2i−2i−2i2i2i−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ140000-221−521−521+521+52−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
χ352222-2-222-2-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−2i−2i2i2i2i2i−2i−2i−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ140000-221−521−521+521+52−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000000
χ362222-2-222-2-2−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−2i−2i2i2i−2i−2i2i2i−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ1400002-2−1+52−1+52−1−52−1−521−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000000
χ372222-2-222-2-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−522i2i−2i−2i2i2i−2i−2i−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ3800002-2−1−52−1−52−1+52−1+521+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000000
χ382222-2-222-2-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−522i2i−2i−2i−2i−2i2i2i−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ380000-221+521+521−521−52−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000000
χ392222-2-222-2-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−2i−2i2i2i2i2i−2i−2i−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ380000-221+521+521−521−52−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000000
χ402222-2-222-2-2−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−2i−2i2i2i−2i−2i2i2i−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ3800002-2−1−52−1−52−1+52−1+521+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000000
χ412222-2-2-2-22222000022222200-2-2-2-2-2-2-2-222220000000000002−2−22000022−2−222−2−2−2−222−2−2222222000000000000000000-2-2000000002−2−2200
χ422222-2-2-2-22222000022222200-2-2-2-2-2-2-2-222220000000000002−2−22000022−2−222−2−2−2−222−2−222-2-2-2-20000000000000000002200000000−222−200
χ432222-2-2-2-22222000022222200-2-2-2-2-2-2-2-22222000000000000−222−20000−2−222−2−22222−2−222−2−22222000000000000000000-2-200000000−222−200
χ442222-2-2-2-22222000022222200-2-2-2-2-2-2-2-22222000000000000−222−20000−2−222−2−22222−2−222−2−2-2-2-2-200000000000000000022000000002−2−2200
χ452-22-22i−2i2-22i−2i222i2i−2i−2i-2-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000002-22-200000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ462-22-22i−2i2-22i−2i222i2i−2i−2i-2-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000002-22-2000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ472-22-22i−2i2-22i−2i22−2i−2i2i2i-2-22-22-2-222i−2i2i−2i2-22-22i−2i2i−2i−2i−2i2i2i−2i−2i2i2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000-22-22000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
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χ1088-8-88000000−2+25−2−25−4i24i24i2−4i22−252+252−25−2+252+25−2−2500000000000000−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ372ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ392ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88000000−2−25−2+254i2−4i2−4i24i22+252−252+25−2−252−25−2+25000000000000002ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ392ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ37000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88000000−2−25−2+25−4i24i24i2−4i22+252−252+25−2−252−25−2+2500000000000000−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ392ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ372ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.