Finite Group Databasebeta

← Group #13104323

Character table — Group #13104323

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size112444444444888888161616161616162020202025254040404040404040404050505080808080100100100100
order12425555101010105102020202010101010101020888822244040404040404040444101020202444
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1111-11111-1-1-1-11-1-111-1-11-1-1-1
χ31111111111111111111111111-1-11111-11-1-1-1-111111-1-1-1-1111-1-1-1
χ41111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111
χ5111-111111111111111-1-1-1-1-1-11111111-1-111111111111-1-1-1-1-11-1-1
χ6111-111111111111111-1-1-1-1-1-1111-1-111-111111-1-1-1-11-1-1-1-111-1-111
χ7111-111111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-111111-1-111-1-1-1-111
χ8111-111111111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1
χ922222222222222222222222220000-2-20000000000-2000000-2000
χ10222-222222222222222-2-2-2-2-2-220000-2-20000000000-20000002000
χ1122-202222222222-2-2-2-2000000-20000220000000000-22200000-200
χ1222-202222222222-2-2-2-2000000-20000220000000000-2-2-200000200
χ1322-202222222222-2-2-2-2000000-20000-2-200000000002000000002i−2i
χ1422-202222222222-2-2-2-2000000-20000-2-20000000000200000000−2i2i
χ152-2002222-2-2-2-22-2000000000002−2i2−i22-20022−2−2i2i2−i2−i202i−2i00000000
χ162-2002222-2-2-2-22-2000000000002−2−i2i22-20022−2−2−i2−i2i2i20−2i2i00000000
χ172-2002222-2-2-2-22-200000000000−22i2−i22-200−2−222i2i2−i2−i20−2i2i00000000
χ182-2002222-2-2-2-22-200000000000−22−i2i22-200−2−222−i2−i2i2i202i−2i00000000
χ194444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5−1+5−1−53−523+52-1-1-122000020−1+52−1−52−1+52−1−520000000−1+52−1−52000000
χ204444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5−1+5−1−53−523+52-1-1-1-2-20000-201−521+521−521+5200000001−521+52000000
χ2144443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+523−523+52−1−5−1+5-1-1-1002200020000−1+52−1−52−1+52−1−5200000−1+52−1−520000
χ2244443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+523−523+52−1−5−1+5-1-1-100-2-2000-200001−521+521−521+52000001−521+520000
χ2344443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−523+523−52−1+5−1−5-1-1-1002200020000−1−52−1+52−1−52−1+5200000−1−52−1+520000
χ2444443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−523+523−52−1+5−1−5-1-1-100-2-2000-200001+521−521+521−52000001+521−520000
χ254444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5−1−5−1+53+523−52-1-1-122000020−1−52−1+52−1−52−1+520000000−1−52−1+52000000
χ264444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5−1−5−1+53+523−52-1-1-1-2-20000-201+521−521+521−5200000001+521−52000000
χ27444-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−51−51+5−3+52−3−5211-1220000-20−1+52−1−52−1+52−1−5200000001−521+52000000
χ28444-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−51−51+5−3+52−3−5211-1-2-20000201−521+521−521+520000000−1+52−1−52000000
χ29444-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52−3+52−3−521+51−511-10022000-20000−1+52−1−52−1+52−1−52000001−521+520000
χ30444-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52−3+52−3−521+51−511-100-2-2000200001−521+521−521+5200000−1+52−1−520000
χ31444-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52−3−52−3+521−51+511-10022000-20000−1−52−1+52−1−52−1+52000001+521−520000
χ32444-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52−3−52−3+521−51+511-100-2-2000200001+521−521+521−5200000−1−52−1+520000
χ33444-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+51+51−5−3−52−3+5211-1220000-20−1−52−1+52−1−52−1+5200000001+521−52000000
χ34444-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+51+51−5−3−52−3+5211-1-2-20000201+521−521+521−520000000−1−52−1+52000000
χ354-4004444-4-4-4-44-4000000000000000-44000000000000000000000
χ368888-2-2-2-2-2-2-2-233-2-2-2-2-2-2-2-2333000000000000000000000000000
χ37888-8-2-2-2-2-2-2-2-233-2-2-2-22222-3-33000000000000000000000000000
χ3888-80-2-2-2-2-2-2-2-233222200005-5-3000000000000000000000000000
χ3988-80-2-2-2-2-2-2-2-23322220000-55-3000000000000000000000000000
χ4088-80−2+25−2−253−53+53−53+5−2+25−2−25-2-2−3+5−3−52−252+250000002000000000000000000000000000
χ4188-803−53+5−2−25−2+25−2−25−2+253−53+5-2-22+252−25−3+5−3−50000002000000000000000000000000000
χ4288-803+53−5−2+25−2−25−2+25−2−253+53−5-2-22−252+25−3−5−3+50000002000000000000000000000000000
χ4388-80−2−25−2+253+53−53+53−5−2−25−2+25-2-2−3−5−3+52+252−250000002000000000000000000000000000
χ448-800−2+25−2−253−53+5−3+5−3−52−252+25-220000000000022−22000000−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39000000000000000
χ458-800−2+25−2−253−53+5−3+5−3−52−252+25-2200000000000−2222000000ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39000000000000000
χ468-8003−53+5−2−25−2+252+252−25−3+5−3−5-2200000000000002i2−2i200000000ζ7+ζ13+ζ23+ζ37ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37−ζ21−ζ29−ζ31−ζ3900000000000
χ478-8003−53+5−2−25−2+252+252−25−3+5−3−5-220000000000000−2i22i200000000−ζ7−ζ13−ζ23−ζ37−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37ζ21+ζ29+ζ31+ζ3900000000000
χ488-8003+53−5−2+25−2−252−252+25−3−5−3+5-2200000000000002i2−2i200000000ζ21+ζ29+ζ31+ζ39ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39−ζ7−ζ13−ζ23−ζ3700000000000
χ498-8003+53−5−2+25−2−252−252+25−3−5−3+5-220000000000000−2i22i200000000−ζ21−ζ29−ζ31−ζ39−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39ζ7+ζ13+ζ23+ζ3700000000000
χ508-800−2−25−2+253+53−5−3−5−3+52+252−25-220000000000022−22000000ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37000000000000000
χ518-800−2−25−2+253+53−5−3−5−3+52+252−25-2200000000000−2222000000−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37000000000000000
χ5216-1600-4-4-4-444446-600000000000000000000000000000000000000

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