Finite Group Databasebeta

← Group #13025890

Character table — Group #13025890

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222444444444455558888888888888888101010101010101010101616161616161616202020202020202020202020202020202020404040404040404040404040
order124424888888884451020204040404022442488102020202020404040404040248888888810102020404040404416161616161616161616161616161616244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i-1-1ii−i−i
χ6111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii-1-1−i−iii
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii11−i−iii
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i11ii−i−i
χ9111111-1-1-1-11111-1-11111-1-1-1-1111111-1-11-1-1-1-11-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ10111111-1-1-1-11111-1-11111-1-1-1-1111111-1-11-1-1-1-11-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111
χ11111111-1-1-1-11111-1-11111-1-1-1-11111-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ12111111-1-1-1-11111-1-11111-1-1-1-11111-1-1111-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ13111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1ii−i−i11−i−iii
χ14111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1−i−iii11ii−i−i
χ15111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11−i−iii-1-1ii−i−i
χ16111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11ii−i−i-1-1−i−iii
χ1711-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i11-1-11-1i−i-1ii−i−i1i−i11-1-1-11ii−i−i11-1-111-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-11-11-1i−ii−ii−i
χ1811-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i11-1-11-1i−i-1ii−i−i1i−i11-1-1-11ii−i−i11-1-111-1-1ii−i−ii−i-1-111−i−iii-1-111−i−iii1-1-11-11i−i−ii−ii
χ1911-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1-11−ii-1ii−i−i1i−i11-1-1-11ii−i−i11-1-1-1-111−i−iiii−i11-1-1ii−i−i11-1-1ii−i−i-11-11-11−ii−ii−ii
χ2011-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i11-1-1-11−ii-1ii−i−i1i−i11-1-1-11ii−i−i11-1-1-1-111−i−iiii−i-1-111−i−iii-1-111−i−iii-111-11-1−iii−ii−i
χ2111-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i-1-1111-1i−i-1ii−i−i1i−i11-1-11-1−i−iii-1-11111-1-1ii−i−i−iiii−i−i-1-111−i−iii11-1-1-11i−i−ii−ii-111-1
χ2211-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i-1-1111-1i−i-1ii−i−i1i−i11-1-11-1−i−iii-1-11111-1-1ii−i−i−ii−i−iii11-1-1ii−i−i-1-111-11−iii−i−ii1-1-11
χ2311-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i-1-111-11−ii-1ii−i−i1i−i11-1-11-1−i−iii-1-111-1-111−i−iii−iiii−i−i-1-111−i−iii11-1-11-1−iii−ii−i1-1-11
χ2411-1-1-11ii−i−i11-1-1i−i11-1-1ii−i−i-1-111-11−ii-1ii−i−i1i−i11-1-11-1−i−iii-1-111-1-111−i−iii−ii−i−iii11-1-1ii−i−i-1-1111-1i−i−iii−i-111-1
χ2511-1-1-11−i−iii11-1-1−ii11-1-1−i−iii11-1-11-1−ii-1−i−iii1−ii11-1-1-11−i−iii11-1-111-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii1-11-11-1−ii−ii−ii
χ2611-1-1-11−i−iii11-1-1−ii11-1-1−i−iii11-1-11-1−ii-1−i−iii1−ii11-1-1-11−i−iii11-1-111-1-1−i−iii−ii-1-111ii−i−i-1-111ii−i−i1-1-11-11−iii−ii−i
χ2711-1-1-11−i−iii11-1-1−ii11-1-1−i−iii11-1-1-11i−i-1−i−iii1−ii11-1-1-11−i−iii11-1-1-1-111ii−i−i−ii11-1-1−i−iii11-1-1−i−iii-11-11-11i−ii−ii−i
χ2811-1-1-11−i−iii11-1-1−ii11-1-1−i−iii11-1-1-11i−i-1−i−iii1−ii11-1-1-11−i−iii11-1-1-1-111ii−i−i−ii-1-111ii−i−i-1-111ii−i−i-111-11-1i−i−ii−ii
χ2911-1-1-11−i−iii11-1-1−ii11-1-1−i−iii-1-1111-1−ii-1−i−iii1−ii11-1-11-1ii−i−i-1-11111-1-1−i−iiii−iii−i−i11-1-1−i−iii-1-111-11i−i−iii−i1-1-11
χ3011-1-1-11−i−iii11-1-1−ii11-1-1−i−iii-1-1111-1−ii-1−i−iii1−ii11-1-11-1ii−i−i-1-11111-1-1−i−iiii−i−i−iii-1-111ii−i−i11-1-1-11−iii−ii−i-111-1
χ3111-1-1-11−i−iii11-1-1−ii11-1-1−i−iii-1-111-11i−i-1−i−iii1−ii11-1-11-1ii−i−i-1-111-1-111ii−i−ii−iii−i−i11-1-1−i−iii-1-1111-1−iii−i−ii-111-1
χ3211-1-1-11−i−iii11-1-1−ii11-1-1−i−iii-1-111-11i−i-1−i−iii1−ii11-1-11-1ii−i−i-1-111-1-111ii−i−ii−i−i−iii-1-111ii−i−i11-1-11-1i−i−ii−ii1-1-11
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χ35222222-2-2-2-2-2-2-2-2222222-2-2-2-222220000222222-2-2-2-2-2-222-2-2-2-2-2-2-2-200000000220000000000000000000000000000
χ36222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-22222222200000000-2-20000000000000000000000000000
χ372222-2-22-22-20000002222222222220000-20000-2-2-20000-2-22-22-2000000000000002−22−22−22−22−22−22−22−2000000000000
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χ412222-2-2-22-220000002222-2-2-2-222220000-20000-2220000-2-2-22-22000000000000002−22−2−22−222−22−2−22−22000000000000
χ422222-2-2-22-220000002222-2-2-2-222220000-20000-2220000-2-2-22-2200000000000000−22−222−22−2−22−222−22−2000000000000
χ432222-2-2-22-220000002222-2-2-2-2-2-2-2-20000-20000-2220000222-22-200000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
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χ574444444444444444-1-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-1-1-1-1-1-1-1000000000000000000000000000000
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χ888-88i−8i000000−4242−4i24i200-22−2i2i−2ζ13+2ζ21+2ζ29−2ζ372ζ13−2ζ21−2ζ29+2ζ372ζ7+2ζ23−2ζ31−2ζ39−2ζ7−2ζ23+2ζ31+2ζ39000000000ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ380002−2i2−i2000000000000000000000000000000000000000000000000
χ898-8−8i8i00000042−42−4i24i200-222i−2i−2ζ7−2ζ23+2ζ31+2ζ392ζ7+2ζ23−2ζ31−2ζ392ζ13−2ζ21−2ζ29+2ζ37−2ζ13+2ζ21+2ζ29−2ζ37000000000ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38000−22i2−i2000000000000000000000000000000000000000000000000
χ908-8−8i8i00000042−42−4i24i200-222i−2i2ζ7+2ζ23−2ζ31−2ζ39−2ζ7−2ζ23+2ζ31+2ζ39−2ζ13+2ζ21+2ζ29−2ζ372ζ13−2ζ21−2ζ29+2ζ37000000000−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38000−22i2−i2000000000000000000000000000000000000000000000000
χ918-8−8i8i000000−42424i2−4i200-222i−2i−2ζ7−2ζ23+2ζ31+2ζ392ζ7+2ζ23−2ζ31−2ζ392ζ13−2ζ21−2ζ29+2ζ37−2ζ13+2ζ21+2ζ29−2ζ37000000000−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ380002−2−i2i2000000000000000000000000000000000000000000000000
χ928-8−8i8i000000−42424i2−4i200-222i−2i2ζ7+2ζ23−2ζ31−2ζ39−2ζ7−2ζ23+2ζ31+2ζ39−2ζ13+2ζ21+2ζ29−2ζ372ζ13−2ζ21−2ζ29+2ζ37000000000ζ4−ζ6−ζ12−ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14+ζ22+ζ28−ζ36+ζ380002−2−i2i2000000000000000000000000000000000000000000000000

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