Finite Group Databasebeta

← Group #12073313

Character table — Group #12073313

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222222244444444888888888888888881010101016161616161616161616161616161616161616161616161616161616202020204040404040404040408080
order1222225510101010101022441010101022444888810101010202020204444241010101010101010202020202020202020204040404040404040444424444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111-1-11111111-11-1-111-1-1-1-1-1-1111111111-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-11-1
χ1011111111111111-1-11111111-11-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-11
χ1111111111111111-1-11111111-11-1-1-1-111-1-1-1-111111111-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-1-1-1-111-11
χ1211111111111111-1-11111111-11-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-1-11111-1-11-1
χ1311111111111111-1-1111111-11-11-111-1-1-1-1-1-111111111-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-11111-1-1-11
χ1411111111111111-1-1111111-11-11-111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1111-1
χ1511111111111111-1-1111111-11-11-1-1-111-1-1-1-1111111111-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1111111-11-11-1-1-111-1-1-1-11111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1-11
χ172222222222222222-2-222220000-200002222-2-2-2-222220000000000-2-20000000000000000-2-222-20000000000
χ182222222222222222-2-222220000-200002222-2-2-2-2-2-2-2-20000000000-2-2000000000000000022-2-220000000000
χ1922222222222222-2-2-2-22222000020000-2-2-2-2-2-2-2-222220000000000220000000000000000-2-2-2-220000000000
χ2022222222222222-2-2-2-22222000020000-2-2-2-2-2-2-2-2-2-2-2-200000000002200000000000000002222-20000000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000022−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ22222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5222222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-21−521+521−521+521−521−521+521+52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-22-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000
χ25222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-22-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−5200002-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ26222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-22-2-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−520000-22−1+52−1−521−521+521−521−521+521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ27222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-222-2-21−521−521+521+52−1+52−1+52−1−52−1−520000-221−521+52−1+52−1−521−521−521+521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−5200002-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000022−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ30222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5222222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52-2-2-2-222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-21+521−521+521−521+521+521−521−52−1−52−1+521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52-2-2-2-22-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000
χ33222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+522-22-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+5200002-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ34222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+522-22-2-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+520000-22−1−52−1+521+521−521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ35222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52-22-22-222-2-21+521+521−521−52−1−52−1−52−1+52−1+520000-221+521−52−1−52−1+521+521+521−521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ36222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52-22-22-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+5200002-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ372222-2-222222222002-2-2-2-2-2020-20000000002-22-222-2-200002200000000-2-20000000000002-2000002-2000000
χ382222-2-222222222002-2-2-2-2-2020-20000000002-22-2-2-22200002200000000-2-2000000000000-2200000-22000000
χ392222-2-222222222002-2-2-2-2-20-2020000000002-22-222-2-20000-2-200000000220000000000002-200000-22000000
χ402222-2-222222222002-2-2-2-2-20-2020000000002-22-2-2-2220000-2-20000000022000000000000-22000002-2000000
χ412222-2-22222222200-22-2-2-2-220-20000000000-22-2222-2-2002200000000-2-200000000000000-220002-200000000
χ422222-2-22222222200-22-2-2-2-220-20000000000-22-22-2-222002200000000-2-2000000000000002-2000-2200000000
χ432222-2-22222222200-22-2-2-2-2-2020000000000-22-2222-2-200-2-2000000002200000000000000-22000-2200000000
χ442222-2-22222222200-22-2-2-2-2-2020000000000-22-22-2-22200-2-20000000022000000000000002-20002-200000000
χ4522-2-22-222-2-2-2-2222-200-2-222000002−22−22-22-200002i−2i2i−2i000000000000000000002−22−22−22−2002i−2i00000i2−i2i2−i200
χ4622-2-22-222-2-2-2-2222-200-2-222000002−22−22-22-20000−2i2i−2i2i000000000000000000002−22−22−22−200−2i2i00000−i2i2−i2i200
χ4722-2-22-222-2-2-2-2222-200-2-22200000−22−222-22-200002i−2i2i−2i00000000000000000000−22−22−22−22002i−2i00000−i2i2−i2i200
χ4822-2-22-222-2-2-2-2222-200-2-22200000−22−222-22-20000−2i2i−2i2i00000000000000000000−22−22−22−2200−2i2i00000i2−i2i2−i200
χ4922-2-22-222-2-2-2-222-2200-2-222000002−2−22-22-2200002i−2i2i−2i000000000000000000002−22−2−22−2200−2i2i00000i2−i2−i2i200
χ5022-2-22-222-2-2-2-222-2200-2-222000002−2−22-22-220000−2i2i−2i2i000000000000000000002−22−2−22−22002i−2i00000−i2i2i2−i200
χ5122-2-22-222-2-2-2-222-2200-2-22200000−222−2-22-2200002i−2i2i−2i00000000000000000000−22−222−22−200−2i2i00000−i2i2i2−i200
χ5222-2-22-222-2-2-2-222-2200-2-22200000−222−2-22-220000−2i2i−2i2i00000000000000000000−22−222−22−2002i−2i00000i2−i2−i2i200
χ53444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−544-4-4−1+5−1−5−1+5−1−50000-40000−1+5−1+5−1−5−1−51−51−51+51+5000000000000001−51+50000000000000000000000000000000
χ54444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−50000400001−51−51+51+51−51−51+51+500000000000000−1+5−1−50000000000000000000000000000000
χ55444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+544-4-4−1−5−1+5−1−5−1+50000-40000−1−5−1−5−1+5−1+51+51+51−51−5000000000000001+51−50000000000000000000000000000000
χ56444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+50000400001+51+51−51−51+51+51−51−500000000000000−1−5−1+50000000000000000000000000000000
χ574444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+5040-4000000000−1+51−5−1−51+500000000−1+5−1−5000000001−51+5000000000000000000000000000
χ584444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+50-404000000000−1+51−5−1−51+5000000001−51+500000000−1+5−1−5000000000000000000000000000
χ594444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+51−51+540-400000000001−5−1+51+5−1−5000000−1+5−1−5000000001−51+500000000000000000000000000000
χ604444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+51−51+5-40400000000001−5−1+51+5−1−50000001−51+500000000−1+5−1−500000000000000000000000000000
χ614444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−5040-4000000000−1−51+5−1+51−500000000−1−5−1+5000000001+51−5000000000000000000000000000
χ624444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−50-404000000000−1−51+5−1+51−5000000001+51−500000000−1−5−1+5000000000000000000000000000
χ634444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−540-400000000001+5−1−51−5−1+5000000−1−5−1+5000000001+51−500000000000000000000000000000
χ644444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−5-40400000000001+5−1−51−5−1+50000001+51−500000000−1−5−1+500000000000000000000000000000
χ6544-4-44-4−1+5−1−51−51−51+51+5−1+5−1−54-4001−51+5−1+5−1−50000022−2222−22−1+51−5−1−51+50000000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000
χ6644-4-44-4−1+5−1−51−51−51+51+5−1+5−1−54-4001−51+5−1+5−1−500000−2222−2222−1+51−5−1−51+50000000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000
χ6744-4-44-4−1+5−1−51−51−51+51+5−1+5−1−5-44001−51+5−1+5−1−50000022−22−22221−5−1+51+5−1−50000000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000
χ6844-4-44-4−1+5−1−51−51−51+51+5−1+5−1−5-44001−51+5−1+5−1−500000−222222−221−5−1+51+5−1−50000000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000
χ6944-4-44-4−1−5−1+51+51+51−51−5−1−5−1+54-4001+51−5−1−5−1+50000022−2222−22−1−51+5−1+51−50000000000000000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ7044-4-44-4−1−5−1+51+51+51−51−5−1−5−1+54-4001+51−5−1−5−1+500000−2222−2222−1−51+5−1+51−50000000000000000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ7144-4-44-4−1−5−1+51+51+51−51−5−1−5−1+5-44001+51−5−1−5−1+50000022−22−22221+5−1−51−5−1+50000000000000000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ7244-4-44-4−1−5−1+51+51+51−51−5−1−5−1+5-44001+51−5−1−5−1+500000−222222−221+5−1−51−5−1+50000000000000000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ7344-4-4-4444-4-4-4-444000044-4-4000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ7444-4-4-4444-4-4-4-444000044-4-400000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ7588-8-8-88−2+25−2−252−252−252+252+25−2+25−2−250000−2+25−2−252−252+250000000000000000000000000000000000000000000000000000000000000000
χ7688-8-8-88−2−25−2+252+252+252−252−25−2−25−2+250000−2−25−2+252+252−250000000000000000000000000000000000000000000000000000000000000000
χ778-88-800888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ788-88-800−2+25−2−25−2+252−25−2−252+252−252+25000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000
χ798-88-800−2+25−2−25−2+252−25−2−252+252−252+2500000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000
χ808-88-800−2−25−2+25−2−252+25−2+252−252+252−2500000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000
χ818-88-800−2−25−2+25−2−252+25−2+252−252+252−25000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000
χ828-8-880088-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800−2+25−2−252−25−2+252+25−2−252−252+250000000000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ848-8-8800−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ858-8-8800−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ868-8-8800−2−25−2+252+25−2−252−25−2+252+252−250000000000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000

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