Finite Group Databasebeta

← Group #12016554

Character table — Group #12016554

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222222222222444444444444444444444444888888888888888888888888888816161616161616161616161616161616161620202020404040404040404040408080
order122222444455101010101010888810101010202020202020202040404040404040408888161616164040404080808080808080808080808080808080442020202020202020404040404040404088882244441616161622
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ91111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111ii−i−i11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1i−iii−i−i1-1
χ101111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111ii−i−i11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111−ii−i−iii-11
χ111111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111ii−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−ii−i−i−i−iiiiiiiii−i−i−i−iii−i−i11-1-1i−i−i−iii-11
χ121111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111ii−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−ii−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-111−iiii−i−i1-1
χ131111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111−i−iii11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111i−iii−i−i-11
χ141111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111−i−iii11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−ii−i−iii1-1
χ151111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111−i−iii-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-111i−i−i−iii1-1
χ161111-1-11-11-1111111111-11-1-1-1-1-111-1-111-1-111111111−i−iii-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii11-1-1−iiii−i−i-11
χ17222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000000000000022220000-2-2000000
χ18222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000000000-2-2-2-2000022000000
χ192222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−520000000000000000
χ202222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+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+52-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ212222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+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+5222−1+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+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+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+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+520000000000000000
χ242222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+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+521−521−521−521−52-2-21+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+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+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+52-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ262222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+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+521−521−521−521−5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ272222-2-22-22-222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ282222-2-22-22-222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ292222-2-22-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522i2i−2i−2i22-2-21−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
χ302222-2-22-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522i2i−2i−2i-2-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
χ312222-2-22-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−2i−2i2i2i22-2-21−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000000
χ322222-2-22-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−2i−2i2i2i-2-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000000000000000
χ332222-2-22-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521−521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522i2i−2i−2i22-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522i−2i−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000000
χ342222-2-22-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521−521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522i2i−2i−2i-2-2221+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−2i2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000000000000000
χ352222-2-22-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521−521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−2i−2i2i2i22-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−2i2iζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000000
χ362222-2-22-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521−521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−2i−2i2i2i-2-2221+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522i−2i−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000000000000000
χ372-2-222-22-2-2222-2-2-2-2220000-2-22222-2-2-2-2220000000000002−22−2000022−2−222−2−222−2−222−2−20000000000000000002-22-20000002−22−200
χ382-2-222-22-2-2222-2-2-2-2220000-2-22222-2-2-2-2220000000000002−22−2000022−2−222−2−222−2−222−2−2000000000000000000-22-22000000−22−2200
χ392-2-222-22-2-2222-2-2-2-2220000-2-22222-2-2-2-222000000000000−22−220000−2−222−2−222−2−222−2−2220000000000000000002-22-2000000−22−2200
χ402-2-222-22-2-2222-2-2-2-2220000-2-22222-2-2-2-222000000000000−22−220000−2−222−2−222−2−222−2−222000000000000000000-22-220000002−22−200
χ412-2-222-2-222-222-2-2-2-22222-2-2-2-222-2-22222-2-22222-2-2-2-22i−2i2i−2i00002-22-2000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ422-2-222-2-222-222-2-2-2-22222-2-2-2-222-2-22222-2-22222-2-2-2-2−2i2i−2i2i00002-22-200000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ432-2-222-2-222-222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-2-2222200000000-22-22000000000000000000000000000000000000002-22-200000000
χ442-2-222-2-222-222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-2-2222200000000-22-2200000000000000000000000000000000000000-22-2200000000
χ452-2-222-2-222-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-21−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+522i−2i2i−2i0000−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ140000000000000000
χ462-2-222-2-222-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-21−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+522i−2i2i−2i0000−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ140000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.