Finite Group Databasebeta

← Group #12020022

Character table — Group #12020022

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1122222444448888888888161616161616161616161616161616161616162020323232323232324040404040808080160
order1225510104441010222420202020202088810101010101020204040404040404040884202020204040244482484
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111-11-1
χ41111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11
χ5111111111111-111-111111111-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-111111-1-1
χ6111111111111-111-111111111-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111
χ7111111111111-111-1111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111-1-11
χ8111111111111-111-1111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1
χ92222222222220-2-20222222000-2-200-2-2000000000022000000000002-2000
χ102222222222220-2-20222222000-2-200-2-20000000000-2-200000000000-22000
χ112222222-2-222202-20-2-222-2-2000-2-2002200000000000000000002200000-20
χ122222222-2-222202-20-2-222-2-2000-2-200220000000000000000000-2-20000020
χ132222222-2-22222-222-2-222-2-200-22222-2-222000000000000000-2-2000000000
χ142222222-2-2222-2-22-2-2-222-2-200222-2-2-2-2-2-200000000000000022000000000
χ15222−1+52−1−52−1+52−1−52222−1+52−1−522222−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52002−1+52−1+52−1−52−1−52−1+52−1−52000000000
χ16222−1+52−1−52−1+52−1−52222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-21−521−521+521+52−1+52−1−52000000000
χ17222−1+52−1−52−1+52−1−52222−1+52−1−52-222-2−1+52−1−52−1+52−1−52−1+52−1−5222-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-21−521−521+521+521−521+52000000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−52-222-2−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2−1+52−1−521−521+52−1+52−1−521−521+521−521−521−521−521+521+521+521+52002−1+52−1+52−1−52−1−521−521+52000000000
χ19222−1+52−1−52−1+52−1−52-2-22−1+52−1−522-2221−521+52−1+52−1−521−521+5200-2−1+52−1−52−1+52−1−521−521+52−1+52−1−52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ141−521+52000000000
χ20222−1+52−1−52−1+52−1−52-2-22−1+52−1−522-2221−521+52−1+52−1−521−521+5200-2−1+52−1−52−1+52−1−521−521+52−1+52−1−52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ141−521+52000000000
χ21222−1+52−1−52−1+52−1−52-2-22−1+52−1−52-2-22-21−521+52−1+52−1−521−521+52002−1+52−1−521−521+521−521+521−521+52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−1+52−1−52000000000
χ22222−1+52−1−52−1+52−1−52-2-22−1+52−1−52-2-22-21−521+52−1+52−1−521−521+52002−1+52−1−521−521+521−521+521−521+52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−1+52−1−52000000000
χ23222−1−52−1+52−1−52−1+52222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+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+52−1+52−1+52002−1−52−1−52−1+52−1+52−1−52−1+52000000000
χ24222−1−52−1+52−1−52−1+52222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-21+521+521−521−52−1−52−1+52000000000
χ25222−1−52−1+52−1−52−1+52222−1−52−1+52-222-2−1−52−1+52−1−52−1+52−1−52−1+5222-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-21+521+521−521−521+521−52000000000
χ26222−1−52−1+52−1−52−1+52222−1−52−1+52-222-2−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2−1−52−1+521+521−52−1−52−1+521+521−521+521+521+521+521−521−521−521−52002−1−52−1−52−1+52−1+521+521−52000000000
χ27222−1−52−1+52−1−52−1+52-2-22−1−52−1+522-2221+521−52−1−52−1+521+521−5200-2−1−52−1+52−1−52−1+521+521−52−1−52−1+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ381+521−52000000000
χ28222−1−52−1+52−1−52−1+52-2-22−1−52−1+522-2221+521−52−1−52−1+521+521−5200-2−1−52−1+52−1−52−1+521+521−52−1−52−1+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ381+521−52000000000
χ29222−1−52−1+52−1−52−1+52-2-22−1−52−1+52-2-22-21+521−52−1−52−1+521+521−52002−1−52−1+521+521−521+521−521+521−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−1−52−1+52000000000
χ30222−1−52−1+52−1−52−1+52-2-22−1−52−1+52-2-22-21+521−52−1−52−1+521+521−52002−1−52−1+521+521−521+521−521+521−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−1−52−1+52000000000
χ31444444400-444000000-4-4000000000000000000000000000000002200-200
χ32444444400-444000000-4-400000000000000000000000000000000-2-200200
χ33444−1+5−1−5−1+5−1−5444−1+5−1−50-4-40−1+5−1−5−1+5−1−5−1+5−1−50001−51+5001−51+50000000000000000000000000000
χ34444−1+5−1−5−1+5−1−5-4-44−1+5−1−504-401−51+5−1+5−1−51−51+50001−51+500−1+5−1−50000000000000000000000000000
χ35444−1−5−1+5−1−5−1+5444−1−5−1+50-4-40−1−5−1+5−1−5−1+5−1−5−1+50001+51−5001+51−50000000000000000000000000000
χ36444−1−5−1+5−1−5−1+5-4-44−1−5−1+504-401+51−5−1−5−1+51+51−50001+51−500−1−5−1+50000000000000000000000000000
χ3744-44444000-4-4200-2000000000002200-2-2000000002200000002-200-20000
χ3844-44444000-4-4200-2000000000002200-2-200000000-2-20000000-220020000
χ3944-44444000-4-4-200200000000000-2-2002200000000220000000-2200-20000
χ4044-44444000-4-4-200200000000000-2-2002200000000-2-200000002-20020000
χ414-4044-4-42-200000002200-2-2i2−i2000000000i2−i2i2−i2i2−i2i2−i222−220000000002i−2i00000
χ424-4044-4-42-200000002200-2-2i2−i2000000000i2−i2i2−i2i2−i2i2−i2−2222000000000−2i2i00000
χ434-4044-4-42-200000002200-2-2−i2i2000000000−i2i2−i2i2−i2i2−i2i222−22000000000−2i2i00000
χ444-4044-4-42-200000002200-2-2−i2i2000000000−i2i2−i2i2−i2i2−i2i2−22220000000002i−2i00000
χ45888−2+25−2−25−2+25−2−2500-8−2+25−2−250000002−252+25000000000000000000000000000000000000000
χ46888−2−25−2+25−2−25−2+2500-8−2−25−2+250000002+252−25000000000000000000000000000000000000000
χ4788-8−2+25−2−25−2+25−2−250002−252+25400-400000000000−1+5−1−5001−51+500000000000000000000000000
χ4888-8−2+25−2−25−2+25−2−250002−252+25-4004000000000001−51+500−1+5−1−500000000000000000000000000
χ4988-8−2−25−2+25−2−25−2+250002+252−25400-400000000000−1−5−1+5001+51−500000000000000000000000000
χ5088-8−2−25−2+25−2−25−2+250002+252−25-4004000000000001+51−500−1−5−1+500000000000000000000000000
χ518-8088-8-8-440000000-4-400440000000000000000000000000000000000000
χ528-80−2+25−2−252−252+254-40000000−1+5−1−5001−51+52i2−2i2000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000
χ538-80−2+25−2−252−252+254-40000000−1+5−1−5001−51+5−2i22i2000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39000000000000000000
χ548-80−2+25−2−252−252+25-4400000001−51+500−1+5−1−500000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ558-80−2+25−2−252−252+25-4400000001−51+500−1+5−1−500000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ568-80−2−25−2+252+252−254-40000000−1−5−1+5001+51−52i2−2i2000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37000000000000000000
χ578-80−2−25−2+252+252−254-40000000−1−5−1+5001+51−5−2i22i2000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37000000000000000000
χ588-80−2−25−2+252+252−25-4400000001+51−500−1−5−1+500000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000000
χ598-80−2−25−2+252+252−25-4400000001+51−500−1−5−1+500000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000000

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