Finite Group Databasebeta

← Group #12072629

Character table — Group #12072629

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222222222444444888888888888888888101016161616161616161616161616161616161616161616161616161616202020404040404040404040408080
order1222225510101010101044101010102244444488202020202020202044481010101020202020202020202020202020204040404040404040224244444448848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-11111-1-11111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ41111111111111111111111-1-11111-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-111-11-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111-111-1-1-11111-1-1
χ6111111111111111111111-111-11-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111-111-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-11-1-11111111-1-1
χ911111111111111111111-1111-1-11-1-1-1-1-1-1-1111111-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-11-111-1-1-11
χ1011111111111111111111-1111-1-11-1-1-1-1-1-1-11111-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1111-1
χ1111111111111111111111-11-1-1-1-11-111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-11-1-1-1111-1
χ1211111111111111111111-11-1-1-1-11-111-1-1-1-11111-1-11-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1111-1-1-11
χ1311111111111111111111-1-1111-1-11-1-111111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1111-1-11-1
χ1411111111111111111111-1-1111-1-11-1-111111111-1-11-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-11
χ1511111111111111111111-1-1-1-11-1-11111111111111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11-11-1-111-11
χ1611111111111111111111-1-1-1-11-1-111111111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-11-111-1-11-1
χ1722222222222222-2-222220000200-200-2-2-2-2-2-2-2-2220000002200000000000000000000-2-2200020-2000000
χ1822222222222222-2-222220000200-200-2-2-2-2-2-2-2-2-2-2000000220000000000000000000022-2000-202000000
χ1922222222222222-2-222220000-2002002222-2-2-2-222000000-2-200000000000000000000-2-22000-202000000
χ2022222222222222-2-222220000-2002002222-2-2-2-2-2-2000000-2-20000000000000000000022-200020-2000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520022−1+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+52−1−5222−1+52−1−52−1+52−1−5222-2-22222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2−1+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+521−521−521+521+52000000000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522-222-22-2-2221−521−521+521+52−1+52−1+52−1−52−1−5200-2-2−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522-2-2-2-22-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−520022−1+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
χ25222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2222-2-22-2-2-21−521−521+521+52−1+52−1+52−1−52−1−5200-221−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ26222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-22-2-2-2-22-2221−521−521+521+52−1+52−1+52−1−52−1−52002-21−521+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
χ27222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-2222-2-22-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002-21−521+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
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-2-2-22-2-2222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-221−521+521−521+52−1+52−1−521−521−521+521+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
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520022−1−52−1+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+5222−1−52−1+52−1−52−1+5222-2-22222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2−1−52−1+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+521−521−521+521+521−521−52000000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522-222-22-2-2221+521+521−521−52−1−52−1−52−1+52−1+5200-2-2−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522-2-2-2-22-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+520022−1−52−1+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
χ33222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2222-2-22-2-2-21+521+521−521−52−1−52−1−52−1+52−1+5200-221+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ34222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-22-2-2-2-22-2221+521+521−521−52−1−52−1−52−1+52−1+52002-21+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
χ35222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-2222-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002-21+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
χ36222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-2-2-22-2-2222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-221+521−521+521−52−1−52−1+521+521+521−521−521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ372222-2-2222222222-2-2-2-2-2020000-200000002-22-22200002200000000-2-20000000000002-2-22000-20000000
χ382222-2-2222222222-2-2-2-2-2020000-200000002-22-2-2-200002200000000-2-2000000000000-222-200020000000
χ392222-2-2222222222-2-2-2-2-20-20000200000002-22-2220000-2-200000000220000000000002-2-2-200020000000
χ402222-2-2222222222-2-2-2-2-20-20000200000002-22-2-2-20000-2-20000000022000000000000-2222000-20000000
χ412222-2-222222222-22-2-2-2-220000-200000000-22-2222002200000000-2-200000000000000-22-20-22000000000
χ422222-2-222222222-22-2-2-2-220000-200000000-22-22-2-2002200000000-2-2000000000000002-2202-2000000000
χ432222-2-222222222-22-2-2-2-2-20000200000000-22-222200-2-2000000002200000000000000-22-202-2000000000
χ442222-2-222222222-22-2-2-2-2-20000200000000-22-22-2-200-2-20000000022000000000000002-220-22000000000
χ45444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−50000400-4001−51−51+51+51−51−51+51+500000000−1+5−1−500000000000000000000000000000000000
χ46444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−50000-400400−1+5−1+5−1−5−1−51−51−51+51+5000000001−51+500000000000000000000000000000000000
χ47444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+50000400-4001+51+51−51−51+51+51−51−500000000−1−5−1+500000000000000000000000000000000000
χ48444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+50000-400400−1−5−1−5−1+5−1+51+51+51−51−5000000001+51−500000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-41−51+51−51+5040000-40000000−1+51−5−1−51+5000000−1+5−1−5000000001−51+5000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-41−51+51−51+50-4000040000000−1+51−5−1−51+50000001−51+500000000−1+5−1−5000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-441−51+51−51+540000-4000000001−5−1+51+5−1−50000−1+5−1−5000000001−51+500000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-441−51+51−51+5-400004000000001−5−1+51+5−1−500001−51+500000000−1+5−1−500000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-41+51−51+51−5040000-40000000−1−51+5−1+51−5000000−1−5−1+5000000001+51−5000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-41+51−51+51−50-4000040000000−1−51+5−1+51−50000001+51−500000000−1−5−1+5000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-441+51−51+51−540000-4000000001+5−1−51−5−1+50000−1−5−1+5000000001+51−500000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-441+51−51+51−5-400004000000001+5−1−51−5−1+500001+51−500000000−1−5−1+500000000000000000000000000000
χ574-44-400444-44-4-4-4000000002i−2i000000000000004-4000000002i−2i2i−2i00000000000000000000000002i−2i0000
χ584-44-400444-44-4-4-4000000002i−2i00000000000000-44000000002i−2i2i−2i0000000000000000000000000−2i2i0000
χ594-44-400444-44-4-4-400000000−2i2i000000000000004-400000000−2i2i−2i2i0000000000000000000000000−2i2i0000
χ604-44-400444-44-4-4-400000000−2i2i00000000000000-4400000000−2i2i−2i2i00000000000000000000000002i−2i0000
χ614-4-444-444-4-4-4-4440044-4-4000000002i2−2i20000000000000000000000000000002i2−2i22i2−2i20000000000000000000
χ624-4-444-444-4-4-4-4440044-4-400000000−2i22i2000000000000000000000000000000−2i22i2−2i22i20000000000000000000
χ634-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+5000000002i2−2i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000
χ644-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+5000000002i2−2i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000
χ654-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+500000000−2i22i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000
χ664-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+500000000−2i22i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000
χ674-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−5000000002i2−2i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000
χ684-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−5000000002i2−2i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000
χ694-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−500000000−2i22i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000
χ704-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−500000000−2i22i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000
χ714-4-44-4444-4-4-4-44400-4-4440000000000000000000000000000000000000000000000000000000000022−2200
χ724-4-44-4444-4-4-4-44400-4-44400000000000000000000000000000000000000000000000000000000000−222200
χ7388-8-80088-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-800−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ7588-8-800−2+25−2−252−25−2+252+25−2−252−252+250000000000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ7688-8-800−2−25−2+252+25−2−252−25−2+252+252−250000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ7788-8-800−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ788-88-800−2+25−2−25−2+252−25−2−252+252−252+25000000004i−4i000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000
χ798-88-800−2+25−2−25−2+252−25−2−252+252−252+2500000000−4i4i0000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000000
χ808-88-800−2−25−2+25−2−252+25−2+252−252+252−25000000004i−4i000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000
χ818-88-800−2−25−2+25−2−252+25−2+252−252+252−2500000000−4i4i0000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000
χ828-8-88-88−2+25−2−252−252−252+252+25−2+25−2−25002−252+25−2+25−2−25000000000000000000000000000000000000000000000000000000000000000
χ838-8-88-88−2−25−2+252+252+252−252−25−2−25−2+25002+252−25−2−25−2+25000000000000000000000000000000000000000000000000000000000000000

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