Finite Group Databasebeta

← Group #13017007

Character table — Group #13017007

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222244444444444444445555555588888888888888101010101010101010101010161616161616161620202020202020202020202020202020202020202020202020202020404040404040
order12222222444444445888810101010101010444444444420202020404040404040404044448888888820202020202020204444888888888888888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii-1-1−i−iii
χ511111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ711111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii11−i−iii
χ811111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−i11ii−i−i
χ9111111111111-1-1-1-111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ10111111111111-1-1-1-111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i11−i−iii
χ12111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii11ii−i−i
χ13111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ14111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1
χ15111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1111111111111−i−i−i−iiiiiii−i−i−i−i−i−iiiii-1-1ii−i−i
χ16111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1111111111111iiii−i−i−i−i−i−iiiiiii−i−i−i−i-1-1−i−iii
χ171-1-1-111-1111-1-1ii−i−i1ii−i−i1-1-1-111-111-1-111-1-11-111-1-1iiii−i−i−i−i-1-111ii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i11-1-111-1-11-1i−ii−i
χ181-1-1-111-1111-1-1ii−i−i1ii−i−i1-1-1-111-111-1-111-1-11-111-1-1iiii−i−i−i−i-1-111−i−iii−i−iiiii−i−i11-1-1ii−i−iii−i−i-1-111-1-111−ii−ii-1-111-1-1111-1−ii−ii
χ191-1-1-111-1111-1-1ii−i−i1ii−i−i1-1-1-111-1-1-111-1-1111-111-1-1iiii−i−i−i−i11-1-111-1-1-1-111ii−i−i11-1-1−i−iii−i−iii−i−iiiii−i−i1-1-11−i−iiiii−i−i-111-1-11
χ201-1-1-111-1111-1-1ii−i−i1ii−i−i1-1-1-111-1-1-111-1-1111-111-1-1iiii−i−i−i−i11-1-1-1-11111-1-1ii−i−i11-1-1−i−iii−i−iiiii−i−i−i−iii-111-1ii−i−i−i−iii-11-111-1
χ211-1-1-111-1111-1-1ii−i−i1−i−iii1-1-1-111-111-1-111-1-1-1111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−iii−i−i-1-111ii−i−i−i−iii11-1-111-1-1i−ii−i-1-111-1-111-11−ii−ii
χ221-1-1-111-1111-1-1ii−i−i1−i−iii1-1-1-111-111-1-111-1-1-1111-1-1−i−i−i−iiiii-1-111−i−iii−i−iiiii−i−i-1-111ii−i−i−i−iii-1-111-1-111−ii−ii11-1-111-1-1-11i−ii−i
χ231-1-1-111-1111-1-1ii−i−i1−i−iii1-1-1-111-1-1-111-1-111-1111-1-1−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11ii−i−i−i−iii1-1-111-1
χ241-1-1-111-1111-1-1ii−i−i1−i−iii1-1-1-111-1-1-111-1-111-1111-1-1−i−i−i−iiiii11-1-1-1-11111-1-1ii−i−i-1-111−i−iiiii−i−iii−i−i−i−iii-111-1−i−iiiii−i−i1-11-1-11
χ251-1-1-111-1111-1-1−i−iii1ii−i−i1-1-1-111-111-1-111-1-1-1111-1-1iiii−i−i−i−i-1-111ii−i−iii−i−i−i−iii-1-111−i−iiiii−i−i-1-111-1-111i−ii−i11-1-111-1-1-11−ii−ii
χ261-1-1-111-1111-1-1−i−iii1ii−i−i1-1-1-111-111-1-111-1-1-1111-1-1iiii−i−i−i−i-1-111−i−iii−i−iii−i−iii-1-111−i−iiiii−i−i11-1-111-1-1−ii−ii-1-111-1-111-11i−ii−i
χ271-1-1-111-1111-1-1−i−iii1ii−i−i1-1-1-111-1-1-111-1-111-1111-1-1iiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11−i−iiiii−i−i1-1-111-1
χ281-1-1-111-1111-1-1−i−iii1ii−i−i1-1-1-111-1-1-111-1-111-1111-1-1iiii−i−i−i−i11-1-1-1-11111-1-1−i−iii-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1ii−i−i−i−iii1-11-1-11
χ291-1-1-111-1111-1-1−i−iii1−i−iii1-1-1-111-111-1-111-1-11-111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i−i−iii11-1-1−i−iii−i−iii-1-111-1-111i−ii−i-1-111-1-1111-1i−ii−i
χ301-1-1-111-1111-1-1−i−iii1−i−iii1-1-1-111-111-1-111-1-11-111-1-1−i−i−i−iiiii-1-111−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii11-1-111-1-1−ii−ii11-1-111-1-11-1−ii−ii
χ311-1-1-111-1111-1-1−i−iii1−i−iii1-1-1-111-1-1-111-1-1111-111-1-1−i−i−i−iiiii11-1-111-1-1-1-111−i−iii11-1-1ii−i−iii−i−iii−i−i−i−iii1-1-11ii−i−i−i−iii-111-1-11
χ321-1-1-111-1111-1-1−i−iii1−i−iii1-1-1-111-1-1-111-1-1111-111-1-1−i−i−i−iiiii11-1-1-1-11111-1-1−i−iii11-1-1ii−i−iii−i−i−i−iiiii−i−i-111-1−i−iiiii−i−i-11-111-1
χ3322222222-2-2-2-200002000022222222222222200-2-2-2-200000000-2-2-2-222222222000000000000000000000000-2-2-2-200000000000000
χ3422222222-2-2-2-200002000022222222222222200-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000
χ3522222222-2-2-2-20000200002222222-2-2-2-2-2-2-2-200-2-2-2-20000000022222i2i2i2i−2i−2i−2i−2i000000000000000000000000−2i−2i2i2i00000000000000
χ3622222222-2-2-2-20000200002222222-2-2-2-2-2-2-2-200-2-2-2-2000000002222−2i−2i−2i−2i2i2i2i2i0000000000000000000000002i2i−2i−2i00000000000000
χ37222-22-2-2-20000000022−22−2222-2-2-2-22222-2-2-2-200000022−2−222−2−200002-22-22-22-20000000000002−22−20000000000002−22−22−22−2000000
χ38222-22-2-2-20000000022−22−2222-2-2-2-22222-2-2-2-200000022−2−222−2−20000-22-22-22-220000000000002−22−2000000000000−22−22−22−22000000
χ39222-22-2-2-20000000022−22−2222-2-2-2-2-2-2-2-2222200000022−2−222−2−200002i−2i2i−2i−2i2i−2i2i000000000000−22−22000000000000i2−i2i2−i2−i2i2−i2i2000000
χ40222-22-2-2-20000000022−22−2222-2-2-2-2-2-2-2-2222200000022−2−222−2−20000−2i2i−2i2i2i−2i2i−2i000000000000−22−22000000000000−i2i2−i2i2i2−i2i2−i2000000
χ41222-22-2-2-2000000002−22−22222-2-2-2-22222-2-2-2-2000000−2−222−2−22200002-22-22-22-2000000000000−22−22000000000000−22−22−22−22000000
χ42222-22-2-2-2000000002−22−22222-2-2-2-22222-2-2-2-2000000−2−222−2−2220000-22-22-22-22000000000000−22−220000000000002−22−22−22−2000000
χ43222-22-2-2-2000000002−22−22222-2-2-2-2-2-2-2-22222000000−2−222−2−22200002i−2i2i−2i−2i2i−2i2i0000000000002−22−2000000000000−i2i2−i2i2i2−i2i2−i2000000
χ44222-22-2-2-2000000002−22−22222-2-2-2-2-2-2-2-22222000000−2−222−2−2220000−2i2i−2i2i2i−2i2i−2i0000000000002−22−2000000000000i2−i2i2−i2−i2i2−i2i2000000
χ4522-22-2-2-222-22-2000020000-22-2-22-222i−2i2i−2i2i−2i2i−2i002-2-22000000002i−2i2i−2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
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χ4822-22-2-2-222-22-2000020000-22-2-22-22−2i2i−2i2i−2i2i−2i2i002-2-2200000000−2i2i−2i2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ4922-22-2-2-22-22-222-22-220000-22-2-22-222i−2i2i−2i2i−2i2i−2i00-222-200000000−2i2i−2i2i000000002-22-200002i−2i2i−2i000000000000000000000000000000
χ5022-22-2-2-22-22-222-22-220000-22-2-22-22−2i2i−2i2i−2i2i−2i2i00-222-2000000002i−2i2i−2i000000002-22-20000−2i2i−2i2i000000000000000000000000000000
χ5122-22-2-2-22-22-22-22-2220000-22-2-22-222i−2i2i−2i2i−2i2i−2i00-222-200000000−2i2i−2i2i00000000-22-220000−2i2i−2i2i000000000000000000000000000000
χ5222-22-2-2-22-22-22-22-2220000-22-2-22-22−2i2i−2i2i−2i2i−2i2i00-222-2000000002i−2i2i−2i00000000-22-2200002i−2i2i−2i000000000000000000000000000000
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χ542-22-2-2-2222-2-22000020000-2-2222-2-22i−2i−2i2i2i−2i−2i2i002-22-200000000−2i2i2i−2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ552-22-2-2-2222-2-22000020000-2-2222-2-2−2i2i2i−2i−2i2i2i−2i002-22-2000000002i−2i−2i2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
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χ592-22-2-2-222-222-2−2i2i2i−2i20000-2-2222-2-22i−2i−2i2i2i−2i−2i2i00-22-22000000002i−2i−2i2i00000000−2i2i2i−2i00002-2-22000000000000000000000000000000
χ602-22-2-2-222-222-2−2i2i2i−2i20000-2-2222-2-2−2i2i2i−2i−2i2i2i−2i00-22-2200000000−2i2i2i−2i00000000−2i2i2i−2i0000-222-2000000000000000000000000000000
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χ622-2-222-22-2000000002i2−i2−i2i22-2-22-2-2222-2-2-2-222000000i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i−2i2i2i−2i000000000000i2−i2−i2i2000000000000−222−2−222−2000000
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χ642-2-222-22-2000000002i2−i2−i2i22-2-22-2-22-2-22222-2-2000000i2i2−i2−i2−i2−i2i2i20000-222-22-2-22000000000000−i2i2i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000
χ652-2-222-22-2000000002−i2i2i2−i22-2-22-2-2222-2-2-2-222000000−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i2i−2i−2i2i000000000000−i2i2i2−i2000000000000−222−2−222−2000000
χ662-2-222-22-2000000002−i2i2i2−i22-2-22-2-2222-2-2-2-222000000−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i−2i2i2i−2i000000000000−i2i2i2−i20000000000002−2−222−2−22000000
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χ722-2-2-222-22-2-2220000200002-2-2-222-2-2-222-2-22200-2-22200000000-2-222-2-22222-2-20000000000000000000000002-2-2200000000000000
χ734444444444444444-14444-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ744444444444444444-1-4-4-4-4-1-1-1-1-1-1-100000000-4-4-1-1-1-111111111000000000000-1-1-1-111110000000000000000000000000000000000
χ75444444444444-4-4-4-4-14444-1-1-1-1-1-1-100000000-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111110000000000000000000000000000000000
χ76444444444444-4-4-4-4-1-4-4-4-4-1-1-1-1-1-1-10000000044-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000000000000000
χ7744-44-4-4-44-44-444-44-4-100001-111-11-100000000001-1-11i5−i5i5−i5i5−i5i5−i5000000000000-11-11i5−i5i5−i50000000000000000000000000000000000
χ7844-44-4-4-44-44-444-44-4-100001-111-11-100000000001-1-11−i5i5−i5i5−i5i5−i5i5000000000000-11-11−i5i5−i5i50000000000000000000000000000000000
χ7944-44-4-4-44-44-44-44-44-100001-111-11-100000000001-1-11i5−i5i5−i5i5−i5i5−i50000000000001-11-1−i5i5−i5i50000000000000000000000000000000000
χ8044-44-4-4-44-44-44-44-44-100001-111-11-100000000001-1-11−i5i5−i5i5−i5i5−i5i50000000000001-11-1i5−i5i5−i50000000000000000000000000000000000
χ8144-4-4-444-40000000040000-44-44-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-444-40000000040000-44-44-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-444-44-4-40000000040000-4-44-4-4444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ844-444-44-4-40000000040000-4-44-4-444−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ854-44-4-4-444-444-44i−4i−4i4i-1000011-1-1-11100000000001-11-15−55−5−55−55000000000000−iii−i−i5i5i5−i50000000000000000000000000000000000
χ864-44-4-4-444-444-44i−4i−4i4i-1000011-1-1-11100000000001-11-1−55−555−55−5000000000000−iii−ii5−i5−i5i50000000000000000000000000000000000
χ874-44-4-4-444-444-4−4i4i4i−4i-1000011-1-1-11100000000001-11-15−55−5−55−55000000000000i−i−iii5−i5−i5i50000000000000000000000000000000000
χ884-44-4-4-444-444-4−4i4i4i−4i-1000011-1-1-11100000000001-11-1−55−555−55−5000000000000i−i−ii−i5i5i5−i50000000000000000000000000000000000
χ894-4-4-444-4444-4-44i4i−4i−4i-14i4i−4i−4i-1111-1-11000000004-4-1-111−i−i−i−iiiii000000000000−i−iii-1-1110000000000000000000000000000000000
χ904-4-4-444-4444-4-44i4i−4i−4i-1−4i−4i4i4i-1111-1-1100000000-44-1-111iiii−i−i−i−i000000000000−i−iii11-1-10000000000000000000000000000000000
χ914-4-4-444-4444-4-4−4i−4i4i4i-14i4i−4i−4i-1111-1-1100000000-44-1-111−i−i−i−iiiii000000000000ii−i−i11-1-10000000000000000000000000000000000
χ924-4-4-444-4444-4-4−4i−4i4i4i-1−4i−4i4i4i-1111-1-11000000004-4-1-111iiii−i−i−i−i000000000000ii−i−i-1-1110000000000000000000000000000000000
χ9388888888-8-8-8-80000-20000-2-2-2-2-2-2-20000000000222200000000000000000000000000000000000000000000000000000000000000
χ94888-88-8-8-800000000-242−4242−42-2-2-2222200000000000000−2−222−2−222000000000000000000000000000000000000000000000000000000
χ95888-88-8-8-800000000-2−4242−4242-2-2-222220000000000000022−2−222−2−2000000000000000000000000000000000000000000000000000000
χ9688-88-8-8-888-88-80000-200002-222-22-20000000000-222-200000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-888-800000000-200002-22-22-2200000000000000i10−i10−i10i10i10−i10−i10i10000000000000000000000000000000000000000000000000000000
χ9888-8-8-888-800000000-200002-22-22-2200000000000000−i10i10i10−i10−i10i10i10−i10000000000000000000000000000000000000000000000000000000
χ998-888-88-8-800000000-2000022-222-2-20000000000000010−10−1010−101010−10000000000000000000000000000000000000000000000000000000
χ1008-888-88-8-800000000-2000022-222-2-200000000000000−101010−1010−10−1010000000000000000000000000000000000000000000000000000000
χ1018-88-8-8-8888-8-880000-2000022-2-2-2220000000000-22-2200000000000000000000000000000000000000000000000000000000000000
χ1028-8-888-88-800000000-24i2−4i2−4i24i2-222-222-200000000000000−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000000000000000000000
χ1038-8-888-88-800000000-2−4i24i24i2−4i2-222-222-200000000000000i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000000000000000000000
χ1048-8-8-888-88-8-8880000-20000-2222-2-22000000000022-2-200000000000000000000000000000000000000000000000000000000000000

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