Finite Group Databasebeta

← Group #12253181

Character table — Group #12253181

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11222444488888888816162244488881616161616161616163232224448888161616161616161616323255101010202020204040404040404040408080
order122442488224481616161624510102020102040401010202040808080801020510102020102040401010202040808080801020222442488224481616161624
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ3111111111-1-1-1-111111-1-1111111111-1-1-1-111111-1-1111111111-1-1-1-111111-1-1111111111-1-1-1-111111-1-1
χ4111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111
χ511111-1-1111-11-1-111-1-11-111111-1-1111-11-1-111-1-11-111111-1-1111-11-1-111-1-11-111111-1-1111-11-1-111-1-11-1
χ611111-1-1111-11-1-1-1-111-1111111-1-1111-11-1-1-1-111-1111111-1-1111-11-1-1-1-111-1111111-1-1111-11-1-1-1-111-11
χ711111-1-111-11-11-111-1-1-1111111-1-111-11-11-111-1-1-1111111-1-111-11-11-111-1-1-1111111-1-111-11-11-111-1-1-11
χ811111-1-111-11-11-1-1-1111-111111-1-111-11-11-1-1-1111-111111-1-111-11-11-1-1-1111-111111-1-111-11-11-1-1-1111-1
χ92222222-2-20000-20000002222222-2-20000-20000002222222-2-20000-20000002222222-2-20000-2000000
χ1022222-2-2-2-20000200000022222-2-2-2-20000200000022222-2-2-2-20000200000022222-2-2-2-200002000000
χ11222-2-22-200000002−22−200222-2-22-200000002−22−200222-2-22-200000002−22−200222-2-22-200000002−22−200
χ12222-2-22-20000000−22−2200222-2-22-20000000−22−2200222-2-22-20000000−22−2200222-2-22-20000000−22−2200
χ13222-2-2-2200000002−2−2200222-2-2-2200000002−2−2200222-2-2-2200000002−2−2200222-2-2-2200000002−2−2200
χ14222-2-2-220000000−222−200222-2-2-220000000−222−200222-2-2-220000000−222−200222-2-2-220000000−222−200
χ1522-2-22002-2020-2000000022-2-22002-2020-2000000022-2-22002-2020-2000000022-2-22002-2020-20000000
χ1622-2-22002-20-202000000022-2-22002-20-202000000022-2-22002-20-202000000022-2-22002-20-2020000000
χ1722-2-2200-2220-20000000022-2-2200-2220-20000000022-2-2200-2220-20000000022-2-2200-2220-200000000
χ1822-2-2200-22-2020000000022-2-2200-22-2020000000022-2-2200-22-2020000000022-2-2200-22-20200000000
χ1944-44-400000000000000044-44-400000000000000044-44-400000000000000044-44-4000000000000000
χ208-80000000000000000008-80000000000000000008-80000000000000000008-8000000000000000000
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ23111111111-1-1-1-111111-1-1111111111-1-1-1-111111-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ24111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-11111-1-1
χ2511111-1-1111-11-1-111-1-11-111111-1-1111-11-1-111-1-11-111111-1-1111-11-1-111-1-11-1-1-1-1-1-111-1-1-11-111-1-111-11
χ2611111-1-1111-11-1-1-1-111-1111111-1-1111-11-1-1-1-111-1111111-1-1111-11-1-1-1-111-11-1-1-1-1-111-1-1-11-11111-1-11-1
χ2711111-1-111-11-11-111-1-1-1111111-1-111-11-11-111-1-1-1111111-1-111-11-11-111-1-1-11-1-1-1-1-111-1-11-11-11-1-1111-1
χ2811111-1-111-11-11-1-1-1111-111111-1-111-11-11-1-1-1111-111111-1-111-11-11-1-1-1111-1-1-1-1-1-111-1-11-11-1111-1-1-11
χ292222222-2-20000-20000002222222-2-20000-20000002222222-2-20000-2000000-2-2-2-2-2-2-22200002000000
χ3022222-2-2-2-20000200000022222-2-2-2-20000200000022222-2-2-2-200002000000-2-2-2-2-222220000-2000000
χ31222-2-22-200000002−22−200222-2-22-200000002−22−200222-2-22-200000002−22−200-2-2-222-220000000−22−2200
χ32222-2-22-20000000−22−2200222-2-22-20000000−22−2200222-2-22-20000000−22−2200-2-2-222-2200000002−22−200
χ33222-2-2-2200000002−2−2200222-2-2-2200000002−2−2200222-2-2-2200000002−2−2200-2-2-2222-20000000−222−200
χ34222-2-2-220000000−222−200222-2-2-220000000−222−200222-2-2-220000000−222−200-2-2-2222-200000002−2−2200
χ3522-2-22002-2020-2000000022-2-22002-2020-2000000022-2-22002-2020-20000000-2-222-200-220-2020000000
χ3622-2-22002-20-202000000022-2-22002-20-202000000022-2-22002-20-2020000000-2-222-200-22020-20000000
χ3722-2-2200-2220-20000000022-2-2200-2220-20000000022-2-2200-2220-200000000-2-222-2002-2-20200000000
χ3822-2-2200-22-2020000000022-2-2200-22-2020000000022-2-2200-22-20200000000-2-222-2002-220-200000000
χ3944-44-400000000000000044-44-400000000000000044-44-4000000000000000-4-44-44000000000000000
χ408-80000000000000000008-80000000000000000008-8000000000000000000-88000000000000000000
χ4122222222222222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000000000
χ4222222222222222-2-2-2-2-2-2−1+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+521−521−521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+5200000000000000000000
χ43222222222-2-2-2-222222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−52−1−521+521+5200000000000000000000
χ44222222222-2-2-2-22-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−521+521+521+521+52−1−52−1−5200000000000000000000
χ4522222-2-2222-22-2-222-2-22-2−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−1+521−521−52−1+52−1+521−521−52−1+521−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−1−521+521+52−1−52−1−521+521+52−1−521+5200000000000000000000
χ4622222-2-2222-22-2-2-2-222-22−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−1+521−521−521−521−52−1+52−1+521−52−1+52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−1−521+521+521+521+52−1−52−1−521+52−1−5200000000000000000000
χ4722222-2-222-22-22-222-2-2-22−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1+52−1+521−521−521−52−1+52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+52−1−52−1−521+521+521+52−1−5200000000000000000000
χ4822222-2-222-22-22-2-2-2222-2−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−521−521−52−1+52−1+52−1+521−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+521+521+52−1−52−1−52−1−521+5200000000000000000000
χ494444444-4-40000-4000000−1+5−1+5−1+5−1+5−1+5−1+5−1+51−51−500001−5000000−1−5−1−5−1−5−1−5−1−5−1−5−1−51+51+500001+500000000000000000000000000
χ5044444-4-4-4-400004000000−1+5−1+5−1+5−1+5−1+51−51−51−51−50000−1+5000000−1−5−1−5−1−5−1−5−1−51+51+51+51+50000−1−500000000000000000000000000
χ51444-4-44-4000000022−2222−2200−1+5−1+5−1+51−51−5−1+51−50000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700−1−5−1−5−1−51+51+5−1−51+50000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000000000
χ52444-4-44-40000000−2222−222200−1+5−1+5−1+51−51−5−1+51−50000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700−1−5−1−5−1−51+51+5−1−51+50000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000000000
χ53444-4-4-44000000022−22−222200−1+5−1+5−1+51−51−51−5−1+50000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700−1−5−1−5−1−51+51+51+5−1−50000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000000000
χ54444-4-4-440000000−222222−2200−1+5−1+5−1+51−51−51−5−1+50000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700−1−5−1−5−1−51+51+51+5−1−50000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000000000
χ5544-4-44004-4040-40000000−1+5−1+51−51−5−1+500−1+51−50−1+501−50000000−1−5−1−51+51+5−1−500−1−51+50−1−501+5000000000000000000000000000
χ5644-4-44004-40-4040000000−1+5−1+51−51−5−1+500−1+51−501−50−1+50000000−1−5−1−51+51+5−1−500−1−51+501+50−1−5000000000000000000000000000
χ5744-4-4400-4440-400000000−1+5−1+51−51−5−1+5001−5−1+5−1+501−500000000−1−5−1−51+51+5−1−5001+5−1−5−1−501+50000000000000000000000000000
χ5844-4-4400-44-40400000000−1+5−1+51−51−5−1+5001−5−1+51−50−1+500000000−1−5−1−51+51+5−1−5001+5−1−51+50−1−50000000000000000000000000000
χ5988-88-8000000000000000−2+25−2+252−25−2+252−25000000000000000−2−25−2−252+25−2−252+2500000000000000000000000000000000000
χ6016-16000000000000000000−4+454−45000000000000000000−4−454+4500000000000000000000000000000000000000
χ6122222222222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+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+5200000000000000000000
χ6222222222222222-2-2-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+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+52−1+52−1+52−1+52−1+521−521−521−521−521−521−5200000000000000000000
χ63222222222-2-2-2-222222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+52−1+521−521−5200000000000000000000
χ64222222222-2-2-2-22-2-2-2-222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−521+521+521+521+52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+521−521−521−521−52−1+52−1+5200000000000000000000
χ6522222-2-2222-22-2-222-2-22-2−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−1−521+521+52−1−52−1−521+521+52−1−521+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−1+521−521−52−1+52−1+521−521−52−1+521−5200000000000000000000
χ6622222-2-2222-22-2-2-2-222-22−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−1−521+521+521+521+52−1−52−1−521+52−1−52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−1+521−521−521−521−52−1+52−1+521−52−1+5200000000000000000000
χ6722222-2-222-22-22-222-2-2-22−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+52−1−52−1−521+521+521+52−1−52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1+52−1+521−521−521−52−1+5200000000000000000000
χ6822222-2-222-22-22-2-2-2222-2−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+521+521+52−1−52−1−52−1−521+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−521−521−52−1+52−1+52−1+521−5200000000000000000000
χ694444444-4-40000-4000000−1−5−1−5−1−5−1−5−1−5−1−5−1−51+51+500001+5000000−1+5−1+5−1+5−1+5−1+5−1+5−1+51−51−500001−500000000000000000000000000
χ7044444-4-4-4-400004000000−1−5−1−5−1−5−1−5−1−51+51+51+51+50000−1−5000000−1+5−1+5−1+5−1+5−1+51−51−51−51−50000−1+500000000000000000000000000
χ71444-4-44-4000000022−2222−2200−1−5−1−5−1−51+51+5−1−51+50000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900−1+5−1+5−1+51−51−5−1+51−50000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000000000
χ72444-4-44-40000000−2222−222200−1−5−1−5−1−51+51+5−1−51+50000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−1+5−1+5−1+51−51−5−1+51−50000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000000000
χ73444-4-4-44000000022−22−222200−1−5−1−5−1−51+51+51+5−1−50000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900−1+5−1+5−1+51−51−51−5−1+50000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000000000
χ74444-4-4-440000000−222222−2200−1−5−1−5−1−51+51+51+5−1−50000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900−1+5−1+5−1+51−51−51−5−1+50000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000000000
χ7544-4-44004-4040-40000000−1−5−1−51+51+5−1−500−1−51+50−1−501+50000000−1+5−1+51−51−5−1+500−1+51−50−1+501−5000000000000000000000000000
χ7644-4-44004-40-4040000000−1−5−1−51+51+5−1−500−1−51+501+50−1−50000000−1+5−1+51−51−5−1+500−1+51−501−50−1+5000000000000000000000000000
χ7744-4-4400-4440-400000000−1−5−1−51+51+5−1−5001+5−1−5−1−501+500000000−1+5−1+51−51−5−1+5001−5−1+5−1+501−50000000000000000000000000000
χ7844-4-4400-44-40400000000−1−5−1−51+51+5−1−5001+5−1−51+50−1−500000000−1+5−1+51−51−5−1+5001−5−1+51−50−1+50000000000000000000000000000
χ7988-88-8000000000000000−2−25−2−252+25−2−252+25000000000000000−2+25−2+252−25−2+252−2500000000000000000000000000000000000
χ8016-16000000000000000000−4−454+45000000000000000000−4+454−4500000000000000000000000000000000000000

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