Finite Group Databasebeta

← Group #13018022

Character table — Group #13018022

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888101010101010161616161616161616161616161616202020202020202020404040404040808080808080
order12224445101010222444224444101010101010202020202020202020488888888244444448888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-1111111111111111-1iiii−i−i−i−i-1-1-1-1-1-1i−iii−i−i
χ411111111111111111-1-1-1-1-1-1111111111111111-1−i−i−i−iiiii-1-1-1-1-1-1−ii−i−iii
χ5111111111111-1-11-1-111111111-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-11-11-1
χ6111111111111-1-11-1-111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ7111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i1-11-111−iii−i−ii
χ8111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii1-11-111i−i−iii−i
χ911111111111-11-1-11-1111111-1-111-1-1111-1-111-1-1111111111-1-11-11-1-1-1-11-11
χ1011111111111-11-1-11-1111111-1-111-1-1111-1-111-1-11-1-1-1-1-1-1-1-1-1-11-11-1111-11-1
χ1111111111111-11-1-11-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1-1iiii−i−i−i−i11-11-11−ii−iii−i
χ1211111111111-11-1-11-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1-1−i−i−i−iiiii11-11-11i−ii−i−ii
χ1311111111111-1-11-1-11111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1
χ1411111111111-1-11-1-11111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111
χ1511111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1iiii−i−i−i−i-11111-1i−i−i−iii
χ1611111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1−i−i−i−iiiii-11111-1−iiii−i−i
χ1722222-2-222220200-202222-2-20022002-2-200-2-200-20000000000-2020000000
χ1822222-2-222220200-20-2-2-2-2220022002-2-200-2-2002000000000020-20000000
χ1922222-2-222220-200202222-2-200-2-2002-2-2002200-2000000000020-20000000
χ2022222-2-222220-20020-2-2-2-22200-2-2002-2-200220020000000000-2020000000
χ212222-22-22222200-20022-2-222220000-22-2-2-20000-2000000000-20200000000
χ222222-22-22222200-200-2-222-2-2220000-22-2-2-20000200000000020-200000000
χ232222-22-22222-20020022-2-222-2-20000-22-2220000-200000000020-200000000
χ242222-22-22222-200200-2-222-2-2-2-20000-22-22200002000000000-20200000000
χ252222-2-22222200200-222-2-2-2-2000022-2-220000-2-220000000020000-2000000
χ262222-2-22222200200-2-2-22222000022-2-220000-2-2-200000000-200002000000
χ272222-2-22222200-200222-2-2-2-20000-2-2-2-22000022200000000-200002000000
χ282222-2-22222200-2002-2-222220000-2-2-2-22000022-20000000020000-2000000
χ294444444-1-1-1-1444444000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ304444444-1-1-1-14-4-44-4-4000000-1-11111-1-1-1-1-11111000000000000000000000
χ314444444-1-1-1-1-44-4-44-400000011-1-111-1-1-111-1-111000000000000000000000
χ324444444-1-1-1-1-4-44-4-440000001111-1-1-1-1-11111-1-1000000000000000000000
χ3344444-4-4-1-1-1-10400-400000005−5-1-15−5-1115−5115−5000000000000000000000
χ3444444-4-4-1-1-1-10400-40000000−55-1-1−55-111−5511−55000000000000000000000
χ3544444-4-4-1-1-1-10-400400000005−511−55-1115−5-1-1−55000000000000000000000
χ3644444-4-4-1-1-1-10-40040000000−55115−5-111−55-1-15−5000000000000000000000
χ374444-44-4-1-1-1-1400-400000000-1-15−55−51-11115−5−55000000000000000000000
χ384444-44-4-1-1-1-1400-400000000-1-1−55−551-1111−555−5000000000000000000000
χ394444-44-4-1-1-1-1-400400000000115−5−551-11-1-15−55−5000000000000000000000
χ404444-44-4-1-1-1-1-40040000000011−555−51-11-1-1−55−55000000000000000000000
χ414444-4-44-1-1-1-100400-40000005−55−5-1-111-1−55−5511000000000000000000000
χ424444-4-44-1-1-1-100400-4000000−55−55-1-111-15−55−511000000000000000000000
χ434444-4-44-1-1-1-100-40040000005−5−551111-1−555−5-1-1000000000000000000000
χ444444-4-44-1-1-1-100-4004000000−555−51111-15−5−55-1-1000000000000000000000
χ4544-4-400044-4-400000000004i−4i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ4644-4-400044-4-400000000004i−4i00000000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ4744-4-400044-4-40000000000−4i4i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ4844-4-400044-4-40000000000−4i4i00000000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ494-44-40004-44-4000000004i−4i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ504-44-40004-44-4000000004i−4i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ514-44-40004-44-400000000−4i4i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ524-44-40004-44-400000000−4i4i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ534-4-440004-4-440000004-4000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ544-4-440004-4-440000004-400000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ554-4-440004-4-44000000-44000000000000000000002-2-222-2-22000000000000
χ564-4-440004-4-44000000-4400000000000000000000-222-2-222-2000000000000
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.