Finite Group Databasebeta

← Group #12014497

Character table — Group #12014497

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444444444445555888888888888888888888888888888101016161616161616161616161616161616161616162020202020202020202040404040404040404040
order1244245510102020202022244444441010202088882488888888101010101010202020202020202020202020202088101020204040404040404040404040404040404088888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111
χ9111111111111111-1-111111-1-111111111-1-1ii−i−iii−i−i11-1-1-1-11111111111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111ii−i−iii−i−i-1-1
χ10111111111111111-1-111111-1-111111111-1-1−i−iii−i−iii11-1-1-1-11111111111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111−i−iii−i−iii-1-1
χ11111111111111111-1-111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-1−i−iii−i−iii11
χ12111111111111111-1-111111-1-11111-1-1-1-1-1-1−i−iii−i−iii11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-1ii−i−iii−i−i11
χ13111111111111111-1-11-1-1-1-1-1-11111111111ii−i−i−i−iii11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-1-1-1ii−i−i−i−iii11
χ14111111111111111-1-11-1-1-1-1-1-11111111111−i−iiiii−i−i11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-1-1-1−i−iiiii−i−i11
χ15111111111111111-1-11-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111111111−i−iiiii−i−i-1-1
χ16111111111111111-1-11-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111111111ii−i−i−i−iii-1-1
χ1711-1-11-11111-1-1-1-1-111111-1-1-1-111-1-1ii−i−i1-1i−ii−ii−ii−i-1-11111111111-1-1-1-1-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−iii−i−ii−iii−i−iii−i−i1-11-11-11-1i−i
χ1811-1-11-11111-1-1-1-1-111111-1-1-1-111-1-1ii−i−i1-1−ii−ii−ii−ii-1-11111111111-1-1-1-1-1-1-1-1i−i11-1-1−i−iii−i−iii−i−iii−i−iiii−iii−i−iii−i−i-11-11-11-11i−i
χ1911-1-11-11111-1-1-1-1-111111-1-1-1-111-1-1−i−iii1-1i−ii−ii−ii−i-1-11111111111-1-1-1-1-1-1-1-1−ii11-1-1ii−i−iii−i−iii−i−iii−i−i−ii−i−iii−i−iii-11-11-11-11−ii
χ2011-1-11-11111-1-1-1-1-111111-1-1-1-111-1-1−i−iii1-1−ii−ii−ii−ii-1-11111111111-1-1-1-1-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii−i−iii−ii−i−iii−i−iii1-11-11-11-1−ii
χ2111-1-11-11111-1-1-1-1-1111-1-111-1-111-1-1ii−i−i-11i−ii−i−ii−ii-1-1111111-1-1-1-11111-1-1-1-1i−i-1-111ii−i−iii−i−i−i−iii−i−iiii−iii−i−i−i−iii1-11-1-11-11−ii
χ2211-1-11-11111-1-1-1-1-1111-1-111-1-111-1-1ii−i−i-11−ii−iii−ii−i-1-1111111-1-1-1-11111-1-1-1-1i−i-1-111−i−iii−i−iiiii−i−iii−i−ii−iii−i−i−i−iii-11-111-11-1−ii
χ2311-1-11-11111-1-1-1-1-1111-1-111-1-111-1-1−i−iii-11i−ii−i−ii−ii-1-1111111-1-1-1-11111-1-1-1-1−ii-1-111ii−i−iii−i−i−i−iii−i−iii−ii−i−iiiii−i−i-11-111-11-1i−i
χ2411-1-11-11111-1-1-1-1-1111-1-111-1-111-1-1−i−iii-11−ii−iii−ii−i-1-1111111-1-1-1-11111-1-1-1-1−ii-1-111−i−iii−i−iiiii−i−iii−i−i−ii−i−iiiii−i−i1-11-1-11-11i−i
χ2511-1-11-11111-1-1-1-1-1-1-1111-1-11111-1-1ii−i−i-111-1-111-1-11-1-1-1-1-1-1111111-1-1-1-11111i−i-1-11111-1-1-1-11111-1-1-1-111i−i−i−iiiii−i−i−iii−i−iii−i−ii
χ2611-1-11-11111-1-1-1-1-1-1-1111-1-11111-1-1ii−i−i-11-111-1-111-1-1-1-1-1-1-1111111-1-1-1-11111i−i-1-111-1-11111-1-1-1-11111-1-1i−i−i−iiiii−i−ii−i−iii−i−ii−ii
χ2711-1-11-11111-1-1-1-1-1-1-1111-1-11111-1-1−i−iii-111-1-111-1-11-1-1-1-1-1-1111111-1-1-1-11111−ii-1-11111-1-1-1-11111-1-1-1-111−iiii−i−i−i−iiii−i−iii−i−iii−i
χ2811-1-11-11111-1-1-1-1-1-1-1111-1-11111-1-1−i−iii-11-111-1-111-1-1-1-1-1-1-1111111-1-1-1-11111−ii-1-111-1-11111-1-1-1-11111-1-1−iiii−i−i−i−iii−iii−i−iii−ii−i
χ2911-1-11-11111-1-1-1-1-1-1-11-1-1111111-1-1ii−i−i1-11-1-11-111-1-1-1-1-1-1-111-1-1-1-111111111i−i11-1-111-1-1-1-111-1-11111-1-1i−i−i−iii−i−iii−iii−ii−i−iii−i
χ3011-1-11-11111-1-1-1-1-1-1-11-1-1111111-1-1ii−i−i1-1-111-11-1-11-1-1-1-1-1-111-1-1-1-111111111i−i11-1-1-1-11111-1-111-1-1-1-111i−i−i−iii−i−iiii−i−ii−iii−ii−i
χ3111-1-11-11111-1-1-1-1-1-1-11-1-1111111-1-1−i−iii1-11-1-11-111-1-1-1-1-1-1-111-1-1-1-111111111−ii11-1-111-1-1-1-111-1-11111-1-1−iiii−i−iii−i−ii−i−ii−iii−i−ii
χ3211-1-11-11111-1-1-1-1-1-1-11-1-1111111-1-1−i−iii1-1-111-11-1-11-1-1-1-1-1-111-1-1-1-111111111−ii11-1-1-1-11111-1-111-1-1-1-111−iiii−i−iii−i−i−iii−ii−i−ii−ii
χ3322222222222222-22-2-200002-2222222220000000000-2-222-2-2-2-20000000022-2-22200000000000000000000-2-22-22-200000000000000
χ3422222222222222-22-2-200002-22222-2-2-2-20000000000-2-222-2-2-2-20000000022-2-2-2-20000000000000000000022-22-2200000000000000
χ3522222222222222-2-22-20000-22222222220000000000-2-2-2-222-2-200000000-2-2222200000000000000000000-2-2-22-2200000000000000
χ3622222222222222-2-22-20000-222222-2-2-2-20000000000-2-2-2-222-2-200000000-2-222-2-200000000000000000000222-22-200000000000000
χ37222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222222222−1+52−1−52−1+52−1−5200002222222222−1+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+52−1−5200−1+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+52−1−5200000000000000000000
χ38222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222222222−1+52−1−52−1+52−1−52000022-2-2-2-2-2-2-2-2−1+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+52−1−5200−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+5200000000000000000000
χ39222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-2-2-2-222−1+52−1−52−1+52−1−520000-2-22222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52001−521+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+5200000000000000000000
χ40222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-2-2-2-222−1+52−1−52−1+52−1−520000-2-2-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52001−521+521−521+521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5200000000000000000000
χ41222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-222222-2-2−1+52−1−52−1+52−1−520000-2-22i2i−2i−2i2i2i−2i−2i−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+52001−521+521−521+52−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ1400000000000000000000
χ42222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-222222-2-2−1+52−1−52−1+52−1−520000-2-2−2i−2i2i2i−2i−2i2i2i−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+52001−521+521−521+52ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ1400000000000000000000
χ43222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-22-2-2-2-2-2-2−1+52−1−52−1+52−1−520000222i2i−2i−2i−2i−2i2i2i−1+52−1−521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+5200−1+52−1−52−1+52−1−52−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ1400000000000000000000
χ44222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-22-2-2-2-2-2-2−1+52−1−52−1+52−1−52000022−2i−2i2i2i2i2i−2i−2i−1+52−1−521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+5200−1+52−1−52−1+52−1−52ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ1400000000000000000000
χ45222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222222222−1−52−1+52−1−52−1+5200002222222222−1−52−1+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+5200−1−52−1+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+5200000000000000000000
χ46222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222222222−1−52−1+52−1−52−1+52000022-2-2-2-2-2-2-2-2−1−52−1+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+5200−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−5200000000000000000000
χ47222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222-2-2-2-222−1−52−1+52−1−52−1+520000-2-22222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52001+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+521−5200000000000000000000
χ48222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222-2-2-2-222−1−52−1+52−1−52−1+520000-2-2-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52001+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+5200000000000000000000
χ49222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-222222-2-2−1−52−1+52−1−52−1+520000-2-22i2i−2i−2i2i2i−2i−2i−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−52001+521−521+521−52−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ3800000000000000000000
χ50222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-222222-2-2−1−52−1+52−1−52−1+520000-2-2−2i−2i2i2i−2i−2i2i2i−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−52001+521−521+521−52ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ3800000000000000000000
χ51222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-22-2-2-2-2-2-2−1−52−1+52−1−52−1+520000222i2i−2i−2i−2i−2i2i2i−1−52−1+521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−5200−1−52−1+52−1−52−1+52−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ3800000000000000000000
χ52222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-22-2-2-2-2-2-2−1−52−1+52−1−52−1+52000022−2i−2i2i2i2i2i−2i−2i−1−52−1+521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−5200−1−52−1+52−1−52−1+52ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ3800000000000000000000
χ5322-2-22-22222-2-2-2-222-2-20000-2222-2-22i2i−2i−2i00000000002222-2-2-2-200000000-2-2222i−2i00000000000000000000−2i2i2i−2i−2i2i00000000000000
χ5422-2-22-22222-2-2-2-222-2-20000-2222-2-2−2i−2i2i2i00000000002222-2-2-2-200000000-2-222−2i2i000000000000000000002i−2i−2i2i2i−2i00000000000000
χ5522-2-22-22222-2-2-2-22-22-200002-222-2-22i2i−2i−2i000000000022-2-222-2-20000000022-2-22i−2i00000000000000000000−2i2i−2i2i2i−2i00000000000000
χ5622-2-22-22222-2-2-2-22-22-200002-222-2-2−2i−2i2i2i000000000022-2-222-2-20000000022-2-2−2i2i000000000000000000002i−2i2i−2i−2i2i00000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.