Finite Group Databasebeta

← Group #13017960

Character table — Group #13017960

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111444444455558888881616161616161616161616161616162020204040404040404040404040404040404040408080
order12224445101010444422244410101010101020202020202020202024424444444448888888888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-11-1-111-1-1-1-111111-1-1-1-1111-11-11-1-111111111-1-1-1-1-1-1
χ41111111111111111-1-11-1-111-1-1-1-111111-1-1-1-1111-11-11-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-11-1-11-1-1-111-1-1111-1-111-1-1111-1-11-11-11111-1-1-1-11111-1-1
χ6111111111111111-11-1-11-1-1-111-1-1111-1-111-1-1111-1-11-11-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-11-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-111
χ8111111111111111-1-11-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1-1-111111111-1-1
χ911111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ1011111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ1111111111111-1-1-1-11-1-11-1-111-1-1-1-111111-1-1-1-1-1-1-11-11-111ii−i−iii−i−i−i−iii−ii
χ1211111111111-1-1-1-11-1-11-1-111-1-1-1-111111-1-1-1-1-1-1-11-11-111−i−iii−i−iiiii−i−ii−i
χ1311111111111-1-1-1-1-11-1-11-1-1-111-1-1111-1-111-1-1-1-1-111-11-11ii−i−i−i−iiiii−i−i−ii
χ1411111111111-1-1-1-1-11-1-11-1-1-111-1-1111-1-111-1-1-1-1-111-11-11−i−iiiii−i−i−i−iiii−i
χ1511111111111-1-1-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-1ii−i−i−i−iii−i−iiii−i
χ1611111111111-1-1-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-1−i−iiiii−i−iii−i−i−ii
χ1722222-2-2222222220200-200022002-2-200-2-200-22-200-202000000000000000
χ1822222-2-2222222220-2002000-2-2002-2-2002200-22-20020-2000000000000000
χ1922222-2-22222-2-2-2-20200-200022002-2-200-2-2002-220020-2000000000000000
χ2022222-2-22222-2-2-2-20-2002000-2-2002-2-20022002-2200-202000000000000000
χ212222-22-222222222200-200220000-22-2-2-20000-2-220-2020000000000000000
χ222222-22-222222222-200200-2-20000-22-2220000-2-22020-20000000000000000
χ232222-22-22222-2-2-2-2200-200220000-22-2-2-2000022-2020-20000000000000000
χ242222-22-22222-2-2-2-2-200200-2-20000-22-222000022-20-2020000000000000000
χ252222-2-222222222200200-2000022-2-220000-2-22-2-2-20000200000000000000
χ262222-2-222222222200-20020000-2-2-2-220000222-2-220000-200000000000000
χ272222-2-222222-2-2-2-200200-2000022-2-220000-2-2-22220000-200000000000000
χ282222-2-222222-2-2-2-200-20020000-2-2-2-22000022-222-20000200000000000000
χ294444444-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444-1-1-1-100004-4-44-4-4-1-11111-1-1-1-1-1111100000000000000000000000
χ314444444-1-1-1-10000-44-4-44-411-1-111-1-1-111-1-11100000000000000000000000
χ324444444-1-1-1-10000-4-44-4-441111-1-1-1-1-11111-1-100000000000000000000000
χ3344444-4-4-1-1-1-100000400-405−5-1-15−5-1115−5115−500000000000000000000000
χ3444444-4-4-1-1-1-100000400-40−55-1-1−55-111−5511−5500000000000000000000000
χ3544444-4-4-1-1-1-100000-400405−511−55-1115−5-1-1−5500000000000000000000000
χ3644444-4-4-1-1-1-100000-40040−55115−5-111−55-1-15−500000000000000000000000
χ374444-44-4-1-1-1-10000400-400-1-15−55−51-11115−5−5500000000000000000000000
χ384444-44-4-1-1-1-10000400-400-1-1−55−551-1111−555−500000000000000000000000
χ394444-44-4-1-1-1-10000-400400115−5−551-11-1-15−55−500000000000000000000000
χ404444-44-4-1-1-1-10000-40040011−555−51-11-1-1−55−5500000000000000000000000
χ414444-4-44-1-1-1-1000000400-45−55−5-1-111-1−55−551100000000000000000000000
χ424444-4-44-1-1-1-1000000400-4−55−55-1-111-15−55−51100000000000000000000000
χ434444-4-44-1-1-1-1000000-40045−5−551111-1−555−5-1-100000000000000000000000
χ444444-4-44-1-1-1-1000000-4004−555−51111-15−5−55-1-100000000000000000000000
χ4544-4-400044-4-44i−4i4i−4i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ4644-4-400044-4-44i−4i4i−4i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ4744-4-400044-4-4−4i4i−4i4i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ4844-4-400044-4-4−4i4i−4i4i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ494-44-40004-44-44i−4i−4i4i00000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ504-44-40004-44-44i−4i−4i4i000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ514-44-40004-44-4−4i4i4i−4i00000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ524-44-40004-44-4−4i4i4i−4i000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ534-4-440004-4-4444-4-40000000000000000000000000000002i−2i2i−2i0000000000
χ544-4-440004-4-4444-4-4000000000000000000000000000000−2i2i−2i2i0000000000
χ554-4-440004-4-44-4-4440000000000000000000000000000002-2-220000000000
χ564-4-440004-4-44-4-444000000000000000000000000000000-222-20000000000
χ571616-16-16000-4-444000000000000000000000000000000000000000000000000
χ5816-1616-16000-44-44000000000000000000000000000000000000000000000000
χ5916-16-1616000-444-4000000000000000000000000000000000000000000000000

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