Finite Group Databasebeta

← Group #11987121

Character table — Group #11987121

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222224444444888888888888888161616161616323232323232323232323232404080808080808080
order12255101044488101082020202020204040404040404040242020202088101040404040404040402248816161616
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1i−i11iiii−i−i−i−i111-1-1ii−i−i
χ61111111111-1-111-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1i−i11iiii−i−i−i−i-1-1-111−i−iii
χ71111111111-1-111-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1−ii11−i−i−i−iiiii111-1-1−i−iii
χ81111111111-1-111-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1−ii11−i−i−i−iiiii-1-1-111ii−i−i
χ922222222222222222222222222222-2-2-2-2-2-200-2-200000000000000000
χ102222222222-2-222-2222222-2-2-2-2-2-2-2-2-22222200-2-200000000000000000
χ11222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000
χ12222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+52000000000
χ13222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+52001−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14000000000
χ14222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+52001−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14000000000
χ15222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-21−521−521+521+522i−2i−1+52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000000
χ16222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-21−521−521+521+52−2i2i−1+52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000000
χ17222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-22−1+52−1+52−1−52−1−52001−521+52ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36000000000
χ18222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-22−1+52−1+52−1−52−1−52001−521+52−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36000000000
χ19222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000
χ20222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521+521−521−521+521+521−521−52000000000
χ21222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−52001+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38000000000
χ22222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−52001+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38000000000
χ23222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-21+521+521−521−522i−2i−1−52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000000
χ24222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-21+521+521−521−52−2i2i−1−52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000000
χ25222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-22−1−52−1−52−1+52−1+52001+521−52−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28000000000
χ26222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-22−1−52−1−52−1+52−1+52001+521−52ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28000000000
χ2744444440-40004400000-4-40000000000000000000000000022-2000000
χ2844444440-40004400000-4-400000000000000000000000000-2-22000000
χ294444444-44-400440-4-4-4-44400000000000000000000000000000000000
χ30444−1+5−1−5−1+5−1−5-44-400−1+5−1−501−51−51+51+5−1+5−1−500000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000
χ31444−1+5−1−5−1+5−1−5-44-400−1+5−1−501−51−51+51+5−1+5−1−50000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000
χ32444−1−5−1+5−1−5−1+5-44-400−1−5−1+501+51+51−51−5−1−5−1+50000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000
χ33444−1−5−1+5−1−5−1+5-44-400−1−5−1+501+51+51−51−5−1−5−1+500000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000
χ3444-4444400022-4-4-200000022-2-222-2-2000000000000000000000002−22−2
χ3544-4444400022-4-4-200000022-2-222-2-200000000000000000000000−22−22
χ3644-44444000-2-2-4-42000000-2-222-2-22200000000000000000000000i2−i2−i2i2
χ3744-44444000-2-2-4-42000000-2-222-2-22200000000000000000000000−i2i2i2−i2
χ384-4044-4-420-22i2−2i20002-22-2002i2−2i2002i2−2i2000000000000000000002-20i2−i20000
χ394-4044-4-420-22i2−2i20002-22-2002i2−2i2002i2−2i200000000000000000000-220−i2i20000
χ404-4044-4-420-2−2i22i20002-22-200−2i22i200−2i22i2000000000000000000002-20−i2i20000
χ414-4044-4-420-2−2i22i20002-22-200−2i22i200−2i22i200000000000000000000-220i2−i20000
χ42888−2+25−2−25−2+25−2−250-8000−2+25−2−25000002−252+2500000000000000000000000000000000000
χ43888−2−25−2+25−2−25−2+250-8000−2−25−2+25000002+252−2500000000000000000000000000000000000
χ4488-8−2+25−2−25−2+25−2−25000442−252+25-4000000−1+5−1+51−51−5−1−5−1−51+51+5000000000000000000000000000
χ4588-8−2+25−2−25−2+25−2−25000-4-42−252+2540000001−51−5−1+5−1+51+51+5−1−5−1−5000000000000000000000000000
χ4688-8−2−25−2+25−2−25−2+25000442+252−25-4000000−1−5−1−51+51+5−1+5−1+51−51−5000000000000000000000000000
χ4788-8−2−25−2+25−2−25−2+25000-4-42+252−2540000001+51+5−1−5−1−51−51−5−1+5−1+5000000000000000000000000000
χ488-8088-8-8-40400000-44-440000000000000000000000000000000000000
χ498-80−2+25−2−252−252+2540-44i2−4i2000−1+51−5−1−51+5002ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37002ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ3900000000000000000000000000000
χ508-80−2+25−2−252−252+2540-4−4i24i2000−1+51−5−1−51+500−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ3700−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ3900000000000000000000000000000
χ518-80−2+25−2−252−252+25-404000001−5−1+51+5−1−500002ζ7−2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ3700−2ζ21+2ζ29−2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ39000000000000000000000000000
χ528-80−2+25−2−252−252+25-404000001−5−1+51+5−1−50000−2ζ7+2ζ13+2ζ23−2ζ372ζ7−2ζ13−2ζ23+2ζ37002ζ21−2ζ29+2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ39000000000000000000000000000
χ538-80−2−25−2+252+252−2540-44i2−4i2000−1−51+5−1+51−5002ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39002ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ3700000000000000000000000000000
χ548-80−2−25−2+252+252−2540-4−4i24i2000−1−51+5−1+51−500−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ3900−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ3700000000000000000000000000000
χ558-80−2−25−2+252+252−25-404000001+5−1−51−5−1+50000−2ζ21+2ζ29−2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ3900−2ζ7+2ζ13+2ζ23−2ζ372ζ7−2ζ13−2ζ23+2ζ37000000000000000000000000000
χ568-80−2−25−2+252+252−25-404000001+5−1−51−5−1+500002ζ21−2ζ29+2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ39002ζ7−2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ37000000000000000000000000000

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