Finite Group Databasebeta

← Group #66097

Character table — Group #66097

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112224422444882244488551010102020112224422444882244488551010102020
order1248844510204040202051020404020202248844224884410102040402020101020404020202248844
χ111111111111111111111111111111111111111111111111111111111
χ211111-1-111111-1-111111-1-111111-1-111111-1-111111-1-111111-1-111111-1-1
χ3111-1-11-1111-1-11-1111-1-11-1111-1-11-1111-1-11-1111-1-11-1111-1-11-1111-1-11-1
χ4111-1-1-11111-1-1-11111-1-1-11111-1-1-11111-1-1-11111-1-1-11111-1-1-11111-1-1-11
χ522-2000022-2000022-2000022-2000022-2000022-2000022-2000022-20000
χ62-202−2002-202−2002-202−2002-202−2002-202−2002-202−2002-202−2002-202−200
χ72-20−22002-20−22002-20−22002-20−22002-20−22002-20−22002-20−22002-20−2200
χ8111111111111111111111-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1
χ911111-1-111111-1-111111-1-1-1-1-1-1-11111111-1-111111-1-111111-1-1-1-1-1-1-111
χ10111-1-11-1111-1-11-1111-1-11-1-1-1-111-11111-1-11-1111-1-11-1111-1-11-1-1-1-111-11
χ11111-1-1-11111-1-1-11111-1-1-11-1-1-1111-1111-1-1-11111-1-1-11111-1-1-11-1-1-1111-1
χ1222-2000022-2000022-20000-2-22000022-2000022-2000022-20000-2-220000
χ132-202−2002-202−2002-202−200-220−22002-202−2002-202−2002-202−200-220−2200
χ142-20−22002-20−22002-20−2200-2202−2002-20−22002-20−22002-20−2200-2202−200
χ152222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000002222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000
χ1622222-2-2−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−521+521+52000000022222-2-2−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−521+521+520000000
χ17222-2-22-2−1+52−1+52−1+521−521−52−1+521−52−1−52−1−52−1−521+521+52−1−521+520000000222-2-22-2−1+52−1+52−1+521−521−52−1+521−52−1−52−1−52−1−521+521+52−1−521+520000000
χ18222-2-2-22−1+52−1+52−1+521−521−521−52−1+52−1−52−1−52−1−521+521+521+52−1−520000000222-2-2-22−1+52−1+52−1+521−521−521−52−1+52−1−52−1−52−1−521+521+521+52−1−520000000
χ1944-40000−1+5−1+51−50000−1−5−1−51+50000000000044-40000−1+5−1+51−50000−1−5−1−51+500000000000
χ204-4022−2200−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000004-4022−2200−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000
χ214-40−222200−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000004-40−222200−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000
χ222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+5200000002222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000
χ2322222-2-2−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+521−521−52000000022222-2-2−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+521−521−520000000
χ24222-2-22-2−1−52−1−52−1−521+521+52−1−521+52−1+52−1+52−1+521−521−52−1+521−520000000222-2-22-2−1−52−1−52−1−521+521+52−1−521+52−1+52−1+52−1+521−521−52−1+521−520000000
χ25222-2-2-22−1−52−1−52−1−521+521+521+52−1−52−1+52−1+52−1+521−521−521−52−1+520000000222-2-2-22−1−52−1−52−1−521+521+521+52−1−52−1+52−1+52−1+521−521−521−52−1+520000000
χ2644-40000−1−5−1−51+50000−1+5−1+51−50000000000044-40000−1−5−1−51+50000−1+5−1+51−500000000000
χ274-4022−2200−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000004-4022−2200−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000
χ284-40−222200−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000004-40−222200−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000
χ291111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3011111-1-111111-1-111111-1-111111-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111
χ31111-1-11-1111-1-11-1111-1-11-1111-1-11-1-1-1-111-11-1-1-111-11-1-1-111-11-1-1-111-11
χ32111-1-1-11111-1-1-11111-1-1-11111-1-1-11-1-1-1111-1-1-1-1111-1-1-1-1111-1-1-1-1111-1
χ3322-2000022-2000022-2000022-20000-2-220000-2-220000-2-220000-2-220000
χ342-202−2002-202−2002-202−2002-202−200-220−2200-220−2200-220−2200-220−2200
χ352-20−22002-20−22002-20−22002-20−2200-2202−200-2202−200-2202−200-2202−200
χ36111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ3711111-1-111111-1-111111-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-11111111-1-1
χ38111-1-11-1111-1-11-1111-1-11-1-1-1-111-11-1-1-111-11-1-1-111-11-1-1-111-11111-1-11-1
χ39111-1-1-11111-1-1-11111-1-1-11-1-1-1111-1-1-1-1111-1-1-1-1111-1-1-1-1111-1111-1-1-11
χ4022-2000022-2000022-20000-2-220000-2-220000-2-220000-2-22000022-20000
χ412-202−2002-202−2002-202−200-220−2200-220−2200-220−2200-220−22002-202−200
χ422-20−22002-20−22002-20−2200-2202−200-2202−200-2202−200-2202−2002-20−2200
χ432222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000-2-2-2-2-2-2-21−521−521−521−521−521−521−521+521+521+521+521+521+521+520000000
χ4422222-2-2−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−521+521+520000000-2-2-2-2-2221−521−521−521−521−52−1+52−1+521+521+521+521+521+52−1−52−1−520000000
χ45222-2-22-2−1+52−1+52−1+521−521−52−1+521−52−1−52−1−52−1−521+521+52−1−521+520000000-2-2-222-221−521−521−52−1+52−1+521−52−1+521+521+521+52−1−52−1−521+52−1−520000000
χ46222-2-2-22−1+52−1+52−1+521−521−521−52−1+52−1−52−1−52−1−521+521+521+52−1−520000000-2-2-2222-21−521−521−52−1+52−1+52−1+521−521+521+521+52−1−52−1−52−1−521+520000000
χ4744-40000−1+5−1+51−50000−1−5−1−51+500000000000-4-4400001−51−5−1+500001+51+5−1−500000000000
χ484-4022−2200−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000-440−2222001−5−1+50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37001+5−1−50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000
χ494-40−222200−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000-44022−22001−5−1+50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37001+5−1−50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000
χ502222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000-2-2-2-2-2-2-21+521+521+521+521+521+521+521−521−521−521−521−521−521−520000000
χ5122222-2-2−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+521−521−520000000-2-2-2-2-2221+521+521+521+521+52−1−52−1−521−521−521−521−521−52−1+52−1+520000000
χ52222-2-22-2−1−52−1−52−1−521+521+52−1−521+52−1+52−1+52−1+521−521−52−1+521−520000000-2-2-222-221+521+521+52−1−52−1−521+52−1−521−521−521−52−1+52−1+521−52−1+520000000
χ53222-2-2-22−1−52−1−52−1−521+521+521+52−1−52−1+52−1+52−1+521−521−521−52−1+520000000-2-2-2222-21+521+521+52−1−52−1−52−1−521+521−521−521−52−1+52−1+52−1+521−520000000
χ5444-40000−1−5−1−51+50000−1+5−1+51−500000000000-4-4400001+51+5−1−500001−51−5−1+500000000000
χ554-4022−2200−1−51+50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900−1+51−50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000-440−2222001+5−1−50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39001−5−1+50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000
χ564-40−222200−1−51+50−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−1+51−50ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000-44022−22001+5−1−50ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39001−5−1+50−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000

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