Finite Group Databasebeta

← Group #12020076

Character table — Group #12020076

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112222244444448888888888888888816161616163232323232323232323232324040404040408080808080
order1225510104448810104482020202020204040404040404040420202020882020404040404040404022444448888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ4111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1
χ51111111111-1-11111-1111111-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11-11-1111-1-11-1
χ61111111111-1-11111-1111111-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-11-11-1-1-111-11
χ71111111111-1-11111-1111111-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-111111-11-1-1-1-1111-1
χ81111111111-1-11111-1111111-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-11111-11-11111-1-1-11
χ922222222222222-2-2222222222222222-2-2-2-2-200-2-20000000000000000000
χ102222222222-2-222-2-2-2222222-2-2-2-2-2-2-2-22-2-2-2-200220000000000000000000
χ112222222-2-2200222-20-2-2-2-22200000000022-2-2000000000000202000000-20
χ122222222-2-2200222-20-2-2-2-22200000000022-2-2000000000000-20-200000020
χ132222222-2-220022-220-2-2-2-222000000000-2-2220000000000000202000000-2
χ142222222-2-220022-220-2-2-2-222000000000-2-2220000000000000-20-20000002
χ15222−1+52−1−52−1+52−1−5222222−1+52−1−52222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000
χ16222−1+52−1−52−1+52−1−5222222−1+52−1−52222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1−52−1+52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+5200000000000
χ17222−1+52−1−52−1+52−1−5222222−1+52−1−52-2-22−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521+521−521+52001−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000000
χ18222−1+52−1−52−1+52−1−5222222−1+52−1−52-2-22−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521+521−521+52001−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000
χ19222−1+52−1−52−1+52−1−52222-2-2−1+52−1−5222-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2−1+52−1−52−1+52−1−522-21−521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000
χ20222−1+52−1−52−1+52−1−52222-2-2−1+52−1−5222-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2−1+52−1−52−1+52−1−52-221−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000
χ21222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5221−521+521−521+5200−1+52−1−52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000000
χ22222−1+52−1−52−1+52−1−52222-2-2−1+52−1−52-2-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5221−521+521−521+5200−1+52−1−52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000000
χ23222−1−52−1+52−1−52−1+5222222−1−52−1+52222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000
χ24222−1−52−1+52−1−52−1+5222222−1−52−1+52222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1+52−1−52−1+52-2-2−1−52−1+521+521+521−521−521+521+521−521−5200000000000
χ25222−1−52−1+52−1−52−1+5222222−1−52−1+52-2-22−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521−521+521−52001+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000000
χ26222−1−52−1+52−1−52−1+5222222−1−52−1+52-2-22−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521−521+521−52001+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000000
χ27222−1−52−1+52−1−52−1+52222-2-2−1−52−1+5222-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2−1−52−1+52−1−52−1+522-21+521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000
χ28222−1−52−1+52−1−52−1+52222-2-2−1−52−1+5222-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2−1−52−1+52−1−52−1+52-221+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000
χ29222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5221+521−521+521−5200−1−52−1+52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000000
χ30222−1−52−1+52−1−52−1+52222-2-2−1−52−1+52-2-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5221+521−521+521−5200−1−52−1+52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000000
χ31444444400-400440000000-4-40000000000000000000000000000022-20000
χ32444444400-400440000000-4-400000000000000000000000000000-2-220000
χ33444−1+5−1−5−1+5−1−5-4-4400−1+5−1−54-401−51−51+51+5−1+5−1−5000000000−1+5−1−51−51+500000000000000000000000
χ34444−1+5−1−5−1+5−1−5-4-4400−1+5−1−5-4401−51−51+51+5−1+5−1−50000000001−51+5−1+5−1−500000000000000000000000
χ35444−1−5−1+5−1−5−1+5-4-4400−1−5−1+54-401+51+51−51−5−1−5−1+5000000000−1−5−1+51+51−500000000000000000000000
χ36444−1−5−1+5−1−5−1+5-4-4400−1−5−1+5-4401+51+51−51−5−1−5−1+50000000001+51−5−1−5−1+500000000000000000000000
χ3744-4444400022-4-400-200000022-2-222-2-20000000000000000022-2-20000000
χ3844-4444400022-4-400-200000022-2-222-2-200000000000000000-2-2220000000
χ3944-44444000-2-2-4-4002000000-2-222-2-222000000000000000002-2-220000000
χ4044-44444000-2-2-4-4002000000-2-222-2-22200000000000000000-222-20000000
χ414-4044-4-42-2022−22000002-22-20022−220022−22000000000000000000000002-202−200
χ424-4044-4-42-2022−22000002-22-20022−220022−2200000000000000000000000-220−2200
χ434-4044-4-42-20−2222000002-22-200−222200−2222000000000000000000000002-20−2200
χ444-4044-4-42-20−2222000002-22-200−222200−222200000000000000000000000-2202−200
χ45888−2+25−2−25−2+25−2−2500-800−2+25−2−2500000002−252+25000000000000000000000000000000000000
χ46888−2−25−2+25−2−25−2+2500-800−2−25−2+2500000002+252−25000000000000000000000000000000000000
χ4788-8−2+25−2−25−2+25−2−25000442−252+2500-4000000−1+5−1+51−51−5−1−5−1−51+51+50000000000000000000000000000
χ4888-8−2+25−2−25−2+25−2−25000-4-42−252+250040000001−51−5−1+5−1+51+51+5−1−5−1−50000000000000000000000000000
χ4988-8−2−25−2+25−2−25−2+25000442+252−2500-4000000−1−5−1−51+51+5−1+5−1+51−51−50000000000000000000000000000
χ5088-8−2−25−2+25−2−25−2+25000-4-42+252−250040000001+51+5−1−5−1−51−51−5−1+5−1+50000000000000000000000000000
χ518-8088-8-8-4400000000-44-4400000000000000000000000000000000000000
χ528-80−2+25−2−252−252+254-4042−4200000−1+51−5−1−51+500−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ37002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ39000000000000000000000000000000
χ538-80−2+25−2−252−252+254-40−424200000−1+51−5−1−51+5002ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ3700−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ39000000000000000000000000000000
χ548-80−2+25−2−252−252+25-44000000001−5−1+51+5−1−50000−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ3700−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ390000000000000000000000000000
χ558-80−2+25−2−252−252+25-44000000001−5−1+51+5−1−500002ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ37002ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ390000000000000000000000000000
χ568-80−2−25−2+252+252−254-4042−4200000−1−51+5−1+51−5002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ3900−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ37000000000000000000000000000000
χ578-80−2−25−2+252+252−254-40−424200000−1−51+5−1+51−500−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ39002ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ37000000000000000000000000000000
χ588-80−2−25−2+252+252−25-44000000001+5−1−51−5−1+50000−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ39002ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ370000000000000000000000000000
χ598-80−2−25−2+252+252−25-44000000001+5−1−51−5−1+500002ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ3900−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ370000000000000000000000000000

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