Finite Group Databasebeta

← Group #12019708

Character table — Group #12019708

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11222224448888888888888888888161616161616161616202032323232323232323232404040808080808080
order1225510104101022488202020202020404040404040404044444101010102420202020202020202020244444448
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11
χ4111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ51111111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1111-111-1-1-1
χ61111111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1111
χ71111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1-111-1
χ81111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111-1-11
χ91111111111-1-111111111111111111-1i−ii−i-1-1-1-111-1-1ii−i−iii−i−i-1-11-1i−ii−i1
χ101111111111-1-111111111111111111-1i−ii−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-11−ii−ii-1
χ111111111111-1-111111111111111111-1−ii−ii-1-1-1-111-1-1−i−iii−i−iii-1-11-1−ii−ii1
χ121111111111-1-111111111111111111-1−ii−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-11i−ii−i-1
χ131111111111-1-11-1-1111111-1-1-1-1-1-1-1-11i−i−ii-1-1-1-11111ii−i−i−i−iii-1-111i−i−ii-1
χ141111111111-1-11-1-1111111-1-1-1-1-1-1-1-11i−i−ii-1-1-1-1-1-111ii−i−i−i−iii11-1-1−iii−i1
χ151111111111-1-11-1-1111111-1-1-1-1-1-1-1-11−iii−i-1-1-1-11111−i−iiiii−i−i-1-111−iii−i-1
χ161111111111-1-11-1-1111111-1-1-1-1-1-1-1-11−iii−i-1-1-1-1-1-111−i−iiiii−i−i11-1-1i−i−ii1
χ1722222222222-2-200-2-2-2-222000000000000022-2-22200000000002-2-2000000
χ1822222222222-2-200-2-2-2-222000000000000022-2-2-2-20000000000-222000000
χ192222222222-22-200-2-2-2-2220000000000000-2-222220000000000-22-2000000
χ202222222222-22-200-2-2-2-2220000000000000-2-222-2-200000000002-22000000
χ21222−1+52−1−52−1+52−1−522−1+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222−1+52−1−52−1+52−1−5200−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000
χ22222−1+52−1−52−1+52−1−522−1+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-2-2-2−1+52−1−52−1+52−1−5200−1+52−1−521−521+521−521+521−521+521−521+52000000000
χ23222−1+52−1−52−1+52−1−522−1+52−1−52222-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222-2-2−1+52−1−52−1+52−1−52001−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000
χ24222−1+52−1−52−1+52−1−522−1+52−1−52222-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2-222−1+52−1−52−1+52−1−52001−521+521−521+521−521+52−1+52−1−52−1+52−1−52000000000
χ25222−1+52−1−52−1+52−1−522−1+52−1−52-2-2222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22i−2i2i−2i1−521+521−521+52001−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000
χ26222−1+52−1−52−1+52−1−522−1+52−1−52-2-2222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2−2i2i−2i2i1−521+521−521+52001−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000
χ27222−1+52−1−52−1+52−1−522−1+52−1−52-2-22-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5222i−2i−2i2i1−521+521−521+5200−1+52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000
χ28222−1+52−1−52−1+52−1−522−1+52−1−52-2-22-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522−2i2i2i−2i1−521+521−521+5200−1+52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000
χ29222−1−52−1+52−1−52−1+522−1−52−1+5222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222222−1−52−1+52−1−52−1+5200−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000
χ30222−1−52−1+52−1−52−1+522−1−52−1+5222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2-2-2-2−1−52−1+52−1−52−1+5200−1−52−1+521+521−521+521−521+521−521+521−52000000000
χ31222−1−52−1+52−1−52−1+522−1−52−1+52222-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222-2-2−1−52−1+52−1−52−1+52001+521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000
χ32222−1−52−1+52−1−52−1+522−1−52−1+52222-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2-222−1−52−1+52−1−52−1+52001+521−521+521−521+521−52−1−52−1+52−1−52−1+52000000000
χ33222−1−52−1+52−1−52−1+522−1−52−1+52-2-2222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22i−2i2i−2i1+521−521+521−52001+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000
χ34222−1−52−1+52−1−52−1+522−1−52−1+52-2-2222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2−2i2i−2i2i1+521−521+521−52001+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000
χ35222−1−52−1+52−1−52−1+522−1−52−1+52-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5222i−2i−2i2i1+521−521+521−5200−1−52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000
χ36222−1−52−1+52−1−52−1+522−1−52−1+52-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522−2i2i2i−2i1+521−521+521−5200−1−52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000
χ374444444-444000000000-4-4000000000000000004-40000000000000000000
χ384444444-444000000000-4-400000000000000000-440000000000000000000
χ39444−1+5−1−5−1+5−1−54−1+5−1−54-4-4001−51−51+51+5−1+5−1−50000000000000−1+5−1−51−51+5000000000000000000000
χ40444−1+5−1−5−1+5−1−54−1+5−1−5-44-4001−51−51+51+5−1+5−1−500000000000001−51+5−1+5−1−5000000000000000000000
χ41444−1−5−1+5−1−5−1+54−1−5−1+54-4-4001+51+51−51−5−1−5−1+50000000000000−1−5−1+51+51−5000000000000000000000
χ42444−1−5−1+5−1−5−1+54−1−5−1+5-44-4001+51+51−51−5−1−5−1+500000000000001+51−5−1−5−1+5000000000000000000000
χ43888−2+25−2−25−2+25−2−25-8−2+25−2−250000000002−252+2500000000000000000000000000000000000000
χ44888−2−25−2+25−2−25−2+25-8−2−25−2+250000000002+252−2500000000000000000000000000000000000000
χ4588-888880-8-80000000000000000000000000000000000000000000000000
χ4688-8−2+25−2−25−2+25−2−2502−252+25000000000002ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ28−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36000000000000000000000000000000
χ4788-8−2+25−2−25−2+25−2−2502−252+2500000000000−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ282ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ36000000000000000000000000000000
χ4888-8−2−25−2+25−2−25−2+2502+252−2500000000000−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28000000000000000000000000000000
χ4988-8−2−25−2+25−2−25−2+2502+252−25000000000002ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ28000000000000000000000000000000
χ508-8088-8-80000002i2−2i20000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ518-8088-8-8000000−2i22i2000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ528-80−2+25−2−252−252+250000002i2−2i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36002ζ13+2ζ23−2ζ13−2ζ232ζ7+2ζ37−2ζ7−2ζ372ζ29+2ζ39−2ζ29−2ζ392ζ21+2ζ31−2ζ21−2ζ31000000000000000000000000000000
χ538-80−2+25−2−252−252+250000002i2−2i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36002ζ7+2ζ37−2ζ7−2ζ372ζ13+2ζ23−2ζ13−2ζ232ζ21+2ζ31−2ζ21−2ζ312ζ29+2ζ39−2ζ29−2ζ39000000000000000000000000000000
χ548-80−2+25−2−252−252+25000000−2i22i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600−2ζ13−2ζ232ζ13+2ζ23−2ζ7−2ζ372ζ7+2ζ37−2ζ29−2ζ392ζ29+2ζ39−2ζ21−2ζ312ζ21+2ζ31000000000000000000000000000000
χ558-80−2+25−2−252−252+25000000−2i22i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600−2ζ7−2ζ372ζ7+2ζ37−2ζ13−2ζ232ζ13+2ζ23−2ζ21−2ζ312ζ21+2ζ31−2ζ29−2ζ392ζ29+2ζ39000000000000000000000000000000
χ568-80−2−25−2+252+252−250000002i2−2i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28002ζ29+2ζ39−2ζ29−2ζ392ζ21+2ζ31−2ζ21−2ζ312ζ7+2ζ37−2ζ7−2ζ372ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000
χ578-80−2−25−2+252+252−250000002i2−2i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28002ζ21+2ζ31−2ζ21−2ζ312ζ29+2ζ39−2ζ29−2ζ392ζ13+2ζ23−2ζ13−2ζ232ζ7+2ζ37−2ζ7−2ζ37000000000000000000000000000000
χ588-80−2−25−2+252+252−25000000−2i22i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800−2ζ29−2ζ392ζ29+2ζ39−2ζ21−2ζ312ζ21+2ζ31−2ζ7−2ζ372ζ7+2ζ37−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000
χ598-80−2−25−2+252+252−25000000−2i22i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800−2ζ21−2ζ312ζ21+2ζ31−2ζ29−2ζ392ζ29+2ζ39−2ζ13−2ζ232ζ13+2ζ23−2ζ7−2ζ372ζ7+2ζ37000000000000000000000000000000

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