Finite Group Databasebeta

← Group #13017972

Character table — Group #13017972

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888101010101010161616161616161616161616161616204040404040404040404040404040404040408080
order12224445101010224444224444101010102020202020202020202020424444444448888888888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ411111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ5111111111111-11-1-1-111111111-1-111111-1-1-1-1-1-11-11-11-1-11111-1-1-1-1-1-1-1-111
χ6111111111111-11-1-1-111111111-1-111111-1-1-1-1-1-11-11-11-1-1-1-1-1-111111111-1-1
χ7111111111111-11-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-11-11-111ii−i−i−i−iii−i−iiii−i
χ8111111111111-11-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-11-11-111−i−iiiii−i−iii−i−i−ii
χ911111111111-11-1-11-1111111-1-111111-1-111-1-1-1-111-1-1-11-11111-1-1-1-11111-1-1
χ1011111111111-11-1-11-1111111-1-111111-1-111-1-1-1-111-1-1-11-1-1-1-1-11111-1-1-1-111
χ1111111111111-11-1-11-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1111-11ii−i−i−i−iiiii−i−i−ii
χ1211111111111-11-1-11-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1111-11−i−iiiii−i−i−i−iiii−i
χ1311111111111-1-1-11-11111111-1-1-1-1111-1-1-1-111111-1-11-1-1111111111-1-1-1-1-1-1
χ1411111111111-1-1-11-11111111-1-1-1-1111-1-1-1-111111-1-11-1-11-1-1-1-1-1-1-1-1111111
χ1511111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-111-111-1ii−i−iii−i−i−i−iii−ii
χ1611111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-111-111-1−i−iii−i−iiiii−i−ii−i
χ1722222-2-2222200020-222-222-200002-2-2000022-2-2-200-200200000000000000
χ1822222-2-2222200020-2-2-22-2-2200002-2-2000022-2-2200200-200000000000000
χ1922222-2-22222000-20222-222-200002-2-20000-2-222-200200-200000000000000
χ2022222-2-22222000-202-2-22-2-2200002-2-20000-2-222200-200200000000000000
χ212222-22-2222220-200022-2-2-2-22200-22-2-2-20000002020-20000000000000000
χ222222-22-2222220-2000-2-222222200-22-2-2-2000000-20-2020000000000000000
χ232222-22-22222-20200022-2-2-2-2-2-200-22-22200000020-2020000000000000000
χ242222-22-22222-202000-2-22222-2-200-22-222000000-2020-20000000000000000
χ252222-2-2222220200-20222-2-220022-2-2200-2-20000-22000-2000000000000000
χ262222-2-2222220200-20-2-2-222-20022-2-2200-2-200002-20002000000000000000
χ272222-2-2222220-20020222-2-2200-2-2-2-2200220000-2-20002000000000000000
χ282222-2-2222220-20020-2-2-222-200-2-2-2-220022000022000-2000000000000000
χ294444444-1-1-1-1444444000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ304444444-1-1-1-14-44-4-4-4000000-1-111-1-1-1-1-1111111000000000000000000000
χ314444444-1-1-1-1-44-4-44-400000011-1-1-1-1-111-1-11111000000000000000000000
χ324444444-1-1-1-1-4-4-44-440000001111-1-1-11111-1-1-1-1000000000000000000000
χ3344444-4-4-1-1-1-100040-40000005−55−5-1115−55−5-1-111000000000000000000000
χ3444444-4-4-1-1-1-100040-4000000−55−55-111−55−55-1-111000000000000000000000
χ3544444-4-4-1-1-1-1000-4040000005−5−55-1115−5−5511-1-1000000000000000000000
χ3644444-4-4-1-1-1-1000-404000000−555−5-111−555−511-1-1000000000000000000000
χ374444-44-4-1-1-1-140-4000000000-1-15−51-1111−555−55−5000000000000000000000
χ384444-44-4-1-1-1-140-4000000000-1-1−551-11115−5−55−55000000000000000000000
χ394444-44-4-1-1-1-1-404000000000115−51-11-1-1−55−55−55000000000000000000000
χ404444-44-4-1-1-1-1-40400000000011−551-11-1-15−55−55−5000000000000000000000
χ414444-4-44-1-1-1-10400-400000005−5-1-111-1−55115−5−55000000000000000000000
χ424444-4-44-1-1-1-10400-40000000−55-1-111-15−511−555−5000000000000000000000
χ434444-4-44-1-1-1-10-400400000005−51111-1−55-1-1−555−5000000000000000000000
χ444444-4-44-1-1-1-10-40040000000−551111-15−5-1-15−5−55000000000000000000000
χ4544-4-400044-4-40000004-40000000000000000000000000000002-22-2000000
χ4644-4-400044-4-40000004-4000000000000000000000000000000-22-22000000
χ4744-4-400044-4-4000000-440000000000000000000000000000002i−2i−2i2i000000
χ4844-4-400044-4-4000000-44000000000000000000000000000000−2i2i2i−2i000000
χ494-44-40004-44-40000000004i−4i0000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ504-44-40004-44-40000000004i−4i00000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ514-44-40004-44-4000000000−4i4i0000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ524-44-40004-44-4000000000−4i4i00000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ534-4-440004-4-4400000000400-400000000000000000000002i−2i2i−2i0000000000
χ544-4-440004-4-4400000000400-40000000000000000000000−2i2i−2i2i0000000000
χ554-4-440004-4-4400000000-400400000000000000000000002-2-220000000000
χ564-4-440004-4-4400000000-40040000000000000000000000-222-20000000000
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.