Finite Group Databasebeta

← Group #13020086

Character table — Group #13020086

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111224444448888881010101010101616161616161616161616203232404040404040404040404040404080808080
order12224444510101044202020202244444820202020204040404042020448888888888884448
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11
χ3111111111111111111111111-1-111111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-111-1
χ5111111111111111111-1-1-1-1-1-111111111111-111-1-1iiii−i−i−i−iii−i−i-1i−i-1
χ6111111111111111111-1-1-1-1-1-111111111111-111-1-1−i−i−i−iiiii−i−iii-1−ii-1
χ7111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iii1−ii1
χ8111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−i1i−i1
χ9111111111111-1-111111111111-11-1-1-1-1-1-1-1-1111-1-111-1-111-1-111111-1-1-1
χ10111111111111-1-111111111111-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1111-1
χ11111111111111-1-11111111111-111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1111
χ12111111111111-1-11111111111-111-1-1-1-111111-1-1-1-1-1-111-1-1111111-1-1-11
χ13111111111111-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i-1−ii1
χ14111111111111-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iii-1i−i1
χ15111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-111ii−i−i−i−iii−i−iii1i−i-1
χ16111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-111−i−iiiii−i−iii−i−i1−ii-1
χ17222222-2-222222-22-2-22222-2-2200-222-2-20000-2002-20000000000000000
χ18222222-2-222222-22-2-22-2-2-222-200-222-2-20000200-220000000000000000
χ19222222-2-22222-222-2-22222-2-2200-2-2-2220000-200-220000000000000000
χ20222222-2-22222-222-2-22-2-2-222-200-2-2-22200002002-20000000000000000
χ212222-2-22-2222200-222-222-222-200-200000000-20000002-2002-200000000
χ222222-2-22-2222200-222-222-222-200-200000000-2000000-2200-2200000000
χ232222-2-22-2222200-222-2-2-22-2-2200-20000000020000002i−2i00−2i2i00000000
χ242222-2-22-2222200-222-2-2-22-2-2200-2000000002000000−2i2i002i−2i00000000
χ252222-2-2-22222200-2-2-2-222-2-2-2-200200000000200002i−2i002i−2i0000000000
χ262222-2-2-22222200-2-2-2-222-2-2-2-20020000000020000−2i2i00−2i2i0000000000
χ272222-2-2-22222200-2-2-2-2-2-2222200200000000-200002-200-220000000000
χ282222-2-2-22222200-2-2-2-2-2-2222200200000000-20000-22002-20000000000
χ2944444444-1-1-1-144-1-1-1-100000044-1-1-1-1-1-1-1-1-10-1-1000000000000000000
χ3044444444-1-1-1-144-1-1-1-1000000-4-4-1-1-1-1-11111011000000000000000000
χ3144444444-1-1-1-1-4-4-1-1-1-10000004-4-1111111110-1-1000000000000000000
χ3244444444-1-1-1-1-4-4-1-1-1-1000000-44-11111-1-1-1-1011000000000000000000
χ33444444-4-4-1-1-1-14-4-111-1000000001-1-11155−5−505−5000000000000000000
χ34444444-4-4-1-1-1-14-4-111-1000000001-1-111−5−5550−55000000000000000000
χ35444444-4-4-1-1-1-1-44-111-100000000111-1-155−5−50−55000000000000000000
χ36444444-4-4-1-1-1-1-44-111-100000000111-1-1−5−55505−5000000000000000000
χ374-44-44-40044-4-400400-44-4-400400000000000000000000000000000000
χ384-44-44-40044-4-400400-4-44400-400000000000000000000000000000000
χ394-44-4-440044-4-400-40044-4400-400000000000000000000000000000000
χ404-44-4-440044-4-400-4004-44-400400000000000000000000000000000000
χ414-4-4400004-44-40000000004i−4i0000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ424-4-4400004-44-40000000004i−4i00000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ434-4-4400004-44-4000000000−4i4i0000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ444-4-4400004-44-4000000000−4i4i00000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ458888-8-88-8-2-2-2-2002-2-2200000000200000000000000000000000000000
χ468888-8-8-88-2-2-2-200222200000000-200000000000000000000000000000
χ4788-8-800008-8-8800000000000000000000000000000000000000000000
χ4888-8-80000-222-200025−2500000000000000ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39000000000000000000000
χ4988-8-80000-222-200025−2500000000000000−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39000000000000000000000
χ5088-8-80000-222-2000−252500000000000000−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39000000000000000000000
χ5188-8-80000-222-2000−252500000000000000ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39000000000000000000000
χ528-88-88-800-2-22200-200200000000025−25000000000000000000000000000
χ538-88-88-800-2-22200-2002000000000−2525000000000000000000000000000
χ548-88-8-8800-2-22200200-2000000000002i5−2i50000000000000000000000000
χ558-88-8-8800-2-22200200-200000000000−2i52i50000000000000000000000000
χ5616-16-16160000-44-4400000000000000000000000000000000000000000000

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