Finite Group Databasebeta

← Group #13104141

Character table — Group #13104141

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1124444444448888888888888888888840404040505050508080808080808080100100100100
order124555581010101051020202020202040404040404040404040404024442488101020202020202016161616
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-111-1-1
χ61111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111-1-111
χ71111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111
χ81111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-11111-1-1
χ9222222222222222222222222222222220000-2-2-2-2000000000000
χ102222222-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022-2-2000000000000
χ1122-222220222222-2-2-2-2-2-200000000000000002-200000000002−22−2
χ1222-222220222222-2-2-2-2-2-200000000000000002-20000000000−22−22
χ1322-222220222222-2-2-2-2-2-20000000000000000-2200000000002−2−22
χ1422-222220222222-2-2-2-2-2-20000000000000000-220000000000−222−2
χ15444−1+5−1−53−523+5243−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−522000000−1+52−1−52−1+52−1−5200000000
χ16444−1+5−1−53−523+5243−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-2-20000001−521+521−521+5200000000
χ17444−1+5−1−53−523+52-43−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-111111−51−5−3+52−3+52−3−52−3−521+51+52-2000000−1+52−1−521−521+5200000000
χ18444−1+5−1−53−523+52-43−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-111111−51−5−3+52−3+52−3−52−3−521+51+5-220000001−521+52−1+52−1−5200000000
χ194443−523+52−1−5−1+54−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-1-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52002200000000−1+52−1−52−1+52−1−520000
χ204443−523+52−1−5−1+54−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-1-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+5200-2-2000000001−521+521−521+520000
χ214443−523+52−1−5−1+5-4−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-11111−3+52−3+521+51+51−51−5−3−52−3−52002-200000000−1+52−1−521−521+520000
χ224443−523+52−1−5−1+5-4−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-11111−3+52−3+521+51+51−51−5−3−52−3−5200-22000000001−521+52−1+52−1−520000
χ234443+523−52−1+5−1−54−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-1-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52002200000000−1−52−1+52−1−52−1+520000
χ244443+523−52−1+5−1−54−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-1-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−5200-2-2000000001+521−521+521−520000
χ254443+523−52−1+5−1−5-4−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-11111−3−52−3−521−51−51+51+5−3+52−3+52002-200000000−1−52−1+521+521−520000
χ264443+523−52−1+5−1−5-4−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-11111−3−52−3−521−51−51+51+5−3+52−3+5200-22000000001+521−52−1−52−1+520000
χ27444−1−5−1+53+523−5243+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+522000000−1−52−1+52−1−52−1+5200000000
χ28444−1−5−1+53+523−5243+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-2-20000001+521−521+521−5200000000
χ29444−1−5−1+53+523−52-43+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-111111+51+5−3−52−3−52−3+52−3+521−51−52-2000000−1−52−1+521+521−5200000000
χ30444−1−5−1+53+523−52-43+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-111111+51+5−3−52−3−52−3+52−3+521−51−5-220000001+521−52−1−52−1+5200000000
χ314-4044440-4-4-4-44-400000000000000000000000022−22000000000000
χ324-4044440-4-4-4-44-4000000000000000000000000−2222000000000000
χ33888-2-2-2-28-2-2-2-233-2-2-2-2333333-2-2-2-2-2-2-2-200000000000000000000
χ34888-2-2-2-2-8-2-2-2-233-2-2-2-233-3-3-3-32222222200000000000000000000
χ3588-8-2-2-2-20-2-2-2-2332222-3-35i5i−5i−5i0000000000000000000000000000
χ3688-8-2-2-2-20-2-2-2-2332222-3-3−5i−5i5i5i0000000000000000000000000000
χ3788-8−2+25−2−253−53+503−53+5−2+25−2−25-2-2−3+5−3−52−252+252200000000000000000000000000000000
χ3888-83−53+5−2−25−2+250−2−25−2+253−53+5-2-22+252−25−3+5−3−52200000000000000000000000000000000
χ3988-83+53−5−2+25−2−250−2+25−2−253+53−5-2-22−252+25−3−5−3+52200000000000000000000000000000000
χ4088-8−2−25−2+253+53−503+53−5−2−25−2+25-2-2−3−5−3+52+252−252200000000000000000000000000000000
χ418-80-2-2-2-2022223-300005i−5iζ13−ζ21−ζ29+ζ37−ζ13+ζ21+ζ29−ζ37−ζ7−ζ23+ζ31+ζ39ζ7+ζ23−ζ31−ζ3910−10i10−i10i10−i1010−1000000000000000000000
χ428-80-2-2-2-2022223-300005i−5i−ζ13+ζ21+ζ29−ζ37ζ13−ζ21−ζ29+ζ37ζ7+ζ23−ζ31−ζ39−ζ7−ζ23+ζ31+ζ39−1010−i10i10−i10i10−101000000000000000000000
χ438-80-2-2-2-2022223-30000−5i5i−ζ7−ζ23+ζ31+ζ39ζ7+ζ23−ζ31−ζ39ζ13−ζ21−ζ29+ζ37−ζ13+ζ21+ζ29−ζ3710−10−i10i10−i10i1010−1000000000000000000000
χ448-80-2-2-2-2022223-30000−5i5iζ7+ζ23−ζ31−ζ39−ζ7−ζ23+ζ31+ζ39−ζ13+ζ21+ζ29−ζ37ζ13−ζ21−ζ29+ζ37−1010i10−i10i10−i10−101000000000000000000000
χ458-80−2+25−2−253−53+50−3+5−3−52−252+25-22000000i10−i10−i10i10002ζ7+2ζ13+3ζ21+2ζ23+3ζ29+3ζ31+2ζ37+3ζ39−2ζ7−2ζ13−3ζ21−2ζ23−3ζ29−3ζ31−2ζ37−3ζ39−3ζ7−3ζ13−2ζ21−3ζ23−2ζ29−2ζ31−3ζ37−2ζ393ζ7+3ζ13+2ζ21+3ζ23+2ζ29+2ζ31+3ζ37+2ζ390000000000000000000000
χ468-80−2+25−2−253−53+50−3+5−3−52−252+25-22000000−i10i10i10−i1000−2ζ7−2ζ13−3ζ21−2ζ23−3ζ29−3ζ31−2ζ37−3ζ392ζ7+2ζ13+3ζ21+2ζ23+3ζ29+3ζ31+2ζ37+3ζ393ζ7+3ζ13+2ζ21+3ζ23+2ζ29+2ζ31+3ζ37+2ζ39−3ζ7−3ζ13−2ζ21−3ζ23−2ζ29−2ζ31−3ζ37−2ζ390000000000000000000000
χ478-803−53+5−2−25−2+2502+252−25−3+5−3−5-2200000010−1010−10−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ3900003ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ39−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ3900000000000000000000
χ488-803−53+5−2−25−2+2502+252−25−3+5−3−5-22000000−1010−10102ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ390000−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ393ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ3900000000000000000000
χ498-803+53−5−2+25−2−2502−252+25−3−5−3+5-2200000010−1010−103ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ39−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ390000−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ3900000000000000000000
χ508-803+53−5−2+25−2−2502−252+25−3−5−3+5-22000000−1010−1010−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ393ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ3900002ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ3900000000000000000000
χ518-80−2−25−2+253+53−50−3−5−3+52+252−25-22000000i10−i10−i10i1000−3ζ7−3ζ13−2ζ21−3ζ23−2ζ29−2ζ31−3ζ37−2ζ393ζ7+3ζ13+2ζ21+3ζ23+2ζ29+2ζ31+3ζ37+2ζ392ζ7+2ζ13+3ζ21+2ζ23+3ζ29+3ζ31+2ζ37+3ζ39−2ζ7−2ζ13−3ζ21−2ζ23−3ζ29−3ζ31−2ζ37−3ζ390000000000000000000000
χ528-80−2−25−2+253+53−50−3−5−3+52+252−25-22000000−i10i10i10−i10003ζ7+3ζ13+2ζ21+3ζ23+2ζ29+2ζ31+3ζ37+2ζ39−3ζ7−3ζ13−2ζ21−3ζ23−2ζ29−2ζ31−3ζ37−2ζ39−2ζ7−2ζ13−3ζ21−2ζ23−3ζ29−3ζ31−2ζ37−3ζ392ζ7+2ζ13+3ζ21+2ζ23+3ζ29+3ζ31+2ζ37+3ζ390000000000000000000000

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