Finite Group Databasebeta

← Group #13016936

Character table — Group #13016936

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12224444444458888101010202020204444444424882020202040404040404040402244101020204040404044444444888888888888448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i
χ91111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111
χ111111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ121111111111111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ131111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii-1-111ii−i−i−i−iii
χ141111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i-1-111−i−iiiii−i−i
χ151111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ161111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111iiii−i−i−i−i11-1-1ii−i−i−i−iii
χ171111-1-1-1-111-1-11i−ii−i111-1-1-1-11111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-111-1-1i−ii−iii−i−iii−i−i1-1i−i1-1i−i1-1i−i
χ181111-1-1-1-111-1-11i−ii−i111-1-1-1-11111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i-1-111-1-111i−ii−i−i−iii−i−iii1-1i−i-11−ii-11−ii
χ191111-1-1-1-111-1-11i−ii−i111-1-1-1-11111-1-1-1-1-11−ii11-1-1ii−i−iii−i−i11-1-1-1-111−i−iii11-1-111-1-1i−ii−iii−i−iii−i−i-11−ii-11−ii-11−ii
χ201111-1-1-1-111-1-11i−ii−i111-1-1-1-11111-1-1-1-1-11−ii11-1-1ii−i−iii−i−i11-1-1-1-111−i−iii-1-111-1-111i−ii−i−i−iii−i−iii-11−ii1-1i−i1-1i−i
χ211111-1-1-1-111-1-11i−ii−i111-1-1-1-1-1-1-1-111111-1i−i11-1-1ii−i−iii−i−i-1-11111-1-1ii−i−iii−i−i−i−iii−ii−ii-1-11111-1-1-11−iii−i-11−ii1-1
χ221111-1-1-1-111-1-11i−ii−i111-1-1-1-1-1-1-1-111111-1i−i11-1-1ii−i−iii−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i−ii−ii11-1-1-1-111-11−ii−ii1-1i−i-11
χ231111-1-1-1-111-1-11i−ii−i111-1-1-1-1-1-1-1-11111-11−ii11-1-1ii−i−iii−i−i-1-111-1-111−i−iiiii−i−i−i−iii−ii−ii-1-11111-1-11-1i−i−ii1-1i−i-11
χ241111-1-1-1-111-1-11i−ii−i111-1-1-1-1-1-1-1-11111-11−ii11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iiiii−i−i−ii−ii11-1-1-1-1111-1i−ii−i-11−ii1-1
χ251111-1-1-1-111-1-11−ii−ii111-1-1-1-11111-1-1-1-11-1−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-111-1-1−ii−ii−i−iii−i−iii1-1−ii1-1−ii1-1−ii
χ261111-1-1-1-111-1-11−ii−ii111-1-1-1-11111-1-1-1-11-1−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii-1-111-1-111−ii−iiii−i−iii−i−i1-1−ii-11i−i-11i−i
χ271111-1-1-1-111-1-11−ii−ii111-1-1-1-11111-1-1-1-1-11i−i11-1-1−i−iii−i−iii11-1-1-1-111ii−i−i11-1-111-1-1−ii−ii−i−iii−i−iii-11i−i-11i−i-11i−i
χ281111-1-1-1-111-1-11−ii−ii111-1-1-1-11111-1-1-1-1-11i−i11-1-1−i−iii−i−iii11-1-1-1-111ii−i−i-1-111-1-111−ii−iiii−i−iii−i−i-11i−i1-1−ii1-1−ii
χ291111-1-1-1-111-1-11−ii−ii111-1-1-1-1-1-1-1-111111-1−ii11-1-1−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i−i−iiii−ii−i11-1-1-1-111-11i−ii−i1-1−ii-11
χ301111-1-1-1-111-1-11−ii−ii111-1-1-1-1-1-1-1-111111-1−ii11-1-1−i−iii−i−iii-1-11111-1-1−i−iii−i−iiiii−i−ii−ii−i-1-11111-1-1-11i−i−ii-11i−i1-1
χ311111-1-1-1-111-1-11−ii−ii111-1-1-1-1-1-1-1-11111-11i−i11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−i−iiii−ii−i11-1-1-1-1111-1−ii−ii-11i−i1-1
χ321111-1-1-1-111-1-11−ii−ii111-1-1-1-1-1-1-1-11111-11i−i11-1-1−i−iii−i−iii-1-111-1-111ii−i−i−i−iiiii−i−ii−ii−i-1-11111-1-11-1−iii−i1-1−ii-11
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χ3522222222-2-2-2-22-2-2222222222222222220000-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000000
χ3622222222-2-2-2-22-2-2222222222-2-2-2-2-2-2-2-20000-2-2-2-22222-2-2-2-222220000000000000000-2-22200000000000000000000
χ372222-2-2-2-2-2-22222i−2i−2i2i222-2-2-2-22222-2-2-2-20000-2-222−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000−2i2i2i−2i00000000000000000000
χ382222-2-2-2-2-2-22222i−2i−2i2i222-2-2-2-2-2-2-2-222220000-2-222−2i−2i2i2i2i2i−2i−2i22-2-200000000000000002i−2i−2i2i00000000000000000000
χ392222-2-2-2-2-2-2222−2i2i2i−2i222-2-2-2-22222-2-2-2-20000-2-2222i2i−2i−2i−2i−2i2i2i-2-22200000000000000002i−2i−2i2i00000000000000000000
χ402222-2-2-2-2-2-2222−2i2i2i−2i222-2-2-2-2-2-2-2-222220000-2-2222i2i−2i−2i−2i−2i2i2i22-2-20000000000000000−2i2i2i−2i00000000000000000000
χ412-22-22i−2i2i−2i2-22i−2i200002-2-22i−2i2i−2i22-2-22i2i−2i−2i00002-22i−2i000000002-22i−2i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ422-22-22i−2i2i−2i2-22i−2i200002-2-22i−2i2i−2i22-2-22i2i−2i−2i00002-22i−2i000000002-22i−2i000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ432-22-22i−2i2i−2i2-22i−2i200002-2-22i−2i2i−2i-2-222−2i−2i2i2i00002-22i−2i00000000-22−2i2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
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χ452-22-22i−2i2i−2i-22−2i2i200002-2-22i−2i2i−2i22-2-22i2i−2i−2i0000-22−2i2i00000000-22−2i2i000000002i−2i2-22i−2i2-2000000000000000000000000
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χ888-88-8−8i8i−8i8i-888i−8i-20000-2222i−2i2i−2i0000000000002-2−2i2i0000000000000000000000000000000000000000000000000000
χ898-8-888i−8i−8i8i0000-200002-222i−2i−2i2i0000000000000000−2ζ7−2ζ23+2ζ31+2ζ392ζ7+2ζ23−2ζ31−2ζ392ζ13−2ζ21−2ζ29+2ζ37−2ζ13+2ζ21+2ζ29−2ζ37000000000000000000000000000000000000000000000000
χ908-8-888i−8i−8i8i0000-200002-222i−2i−2i2i00000000000000002ζ7+2ζ23−2ζ31−2ζ39−2ζ7−2ζ23+2ζ31+2ζ39−2ζ13+2ζ21+2ζ29−2ζ372ζ13−2ζ21−2ζ29+2ζ37000000000000000000000000000000000000000000000000
χ918-8-88−8i8i8i−8i0000-200002-22−2i2i2i−2i00000000000000002ζ13−2ζ21−2ζ29+2ζ37−2ζ13+2ζ21+2ζ29−2ζ37−2ζ7−2ζ23+2ζ31+2ζ392ζ7+2ζ23−2ζ31−2ζ39000000000000000000000000000000000000000000000000
χ928-8-88−8i8i8i−8i0000-200002-22−2i2i2i−2i0000000000000000−2ζ13+2ζ21+2ζ29−2ζ372ζ13−2ζ21−2ζ29+2ζ372ζ7+2ζ23−2ζ31−2ζ39−2ζ7−2ζ23+2ζ31+2ζ39000000000000000000000000000000000000000000000000

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