Finite Group Databasebeta

← Group #13017903

Character table — Group #13017903

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888101010101616161616161616161616162020404040404040404040404040404080808080
order12222445101010244444101010101010444420202020202020202020202044224444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ411111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ5111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-1-1-1-1-111
χ6111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1-1111111-1-1
χ7111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11ii−i−i−i−iii−iii−i
χ8111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11−i−iiiii−i−ii−i−ii
χ911111111111-11-1-11-111-1-1-1-1111111-1-11111-1-1-1-111-11-11-1-11111-1-1-1-111-1-1
χ1011111111111-11-1-11-111-1-1-1-1111111-1-11111-1-1-1-111-11-11-1-1-1-1-1-11111-1-111
χ1111111111111-11-1-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-111ii−i−i−i−iiii−i−ii
χ1211111111111-11-1-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-111−i−iiiii−i−i−iii−i
χ1311111111111-1-11-1-1111-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1111111111-1-1-1-1
χ1411111111111-1-11-1-1111-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-11-1-1-1-1-1-1-1-11111
χ1511111111111-1-11-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-111-1ii−i−iii−i−i−ii−ii
χ1611111111111-1-11-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-111-1−i−iii−i−iiii−ii−i
χ1722222-2-22222200-2002222222-2-22-2-2-2-200000000-222000-20000000000000
χ1822222-2-22222200-200222222-222-2-2-2-2-2000000002-2-200020000000000000
χ1922222-2-22222-20020022-2-2-2-22-2-22-2-22200000000-22-200020000000000000
χ2022222-2-22222-20020022-2-2-2-2-222-2-2-222000000002-22000-20000000000000
χ212222-22-2222200200-2-2-200002-2-222-200000022-2-22-200200-2000000000000
χ222222-22-2222200200-2-2-20000-222-22-200000022-2-2-2200-2002000000000000
χ232222-22-2222200-2002-2-200002-2-222-2000000-2-2222-200-2002000000000000
χ242222-22-2222200-2002-2-20000-222-22-2000000-2-222-2200200-2000000000000
χ252222-2-2222220200-20-2-200002222-220022-2-20000-2-20-20200000000000000
χ262222-2-2222220200-20-2-20000-2-2-2-2-220022-2-2000022020-200000000000000
χ272222-2-2222220-20020-2-200002222-2200-2-2220000-2-2020-200000000000000
χ282222-2-2222220-20020-2-20000-2-2-2-2-2200-2-2220000220-20200000000000000
χ294444444-1-1-1-1444444-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ304444444-1-1-1-14-4-44-4-4-1-1-1-1-1-10000-1-1-1-11111111100000000000000000000
χ314444444-1-1-1-1-44-4-44-4-1-111110000-1-111-1-1-1-1111100000000000000000000
χ324444444-1-1-1-1-4-44-4-44-1-111110000-1-1111111-1-1-1-100000000000000000000
χ3344444-4-4-1-1-1-1400-400-1-1-1-1-1-1000011115−55−55−55−500000000000000000000
χ3444444-4-4-1-1-1-1400-400-1-1-1-1-1-100001111−55−55−55−5500000000000000000000
χ3544444-4-4-1-1-1-1-400400-1-11111000011-1-15−55−5−55−5500000000000000000000
χ3644444-4-4-1-1-1-1-400400-1-11111000011-1-1−55−555−55−500000000000000000000
χ374444-44-4-1-1-1-100400-41155−5−50000-115−55−5−55-1-11100000000000000000000
χ384444-44-4-1-1-1-100400-411−5−5550000-11−55−555−5-1-11100000000000000000000
χ394444-44-4-1-1-1-100-40041155−5−50000-115−5−555−511-1-100000000000000000000
χ404444-44-4-1-1-1-100-400411−5−5550000-11−555−5−5511-1-100000000000000000000
χ414444-4-44-1-1-1-10400-401155−5−500001-1−55-1-1115−5−5500000000000000000000
χ424444-4-44-1-1-1-10400-4011−5−55500001-15−5-1-111−555−500000000000000000000
χ434444-4-44-1-1-1-10-400401155−5−500001-1−5511-1-1−555−500000000000000000000
χ444444-4-44-1-1-1-10-4004011−5−55500001-15−511-1-15−5−5500000000000000000000
χ4544-4-40004-44-400000000000004i−4i000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ4644-4-40004-44-400000000000004i−4i0000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ4744-4-40004-44-40000000000000−4i4i000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ4844-4-40004-44-40000000000000−4i4i0000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ494-4-440004-4-44000000000000400-40000000000000000000000002i−2i2i−2i0000
χ504-4-440004-4-44000000000000400-4000000000000000000000000−2i2i−2i2i0000
χ514-4-440004-4-44000000000000-40040000000000000000000000002-2-220000
χ524-4-440004-4-44000000000000-4004000000000000000000000000-222-20000
χ538-88-800088-8-8000000000000000000000000000000000000000000000000
χ548-88-8000-2-22200000025−25−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36000000000000000000000000000000000000
χ558-88-8000-2-22200000025−252ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36000000000000000000000000000000000000
χ568-88-8000-2-222000000−2525−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ36000000000000000000000000000000000000
χ578-88-8000-2-222000000−25252ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36000000000000000000000000000000000000
χ581616-16-16000-44-44000000000000000000000000000000000000000000000000
χ5916-16-1616000-444-4000000000000000000000000000000000000000000000000

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