Finite Group Databasebeta

← Group #12072744

Character table — Group #12072744

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222222222444444888888888888888888101016161616161616161616161616161616161616161616161616161616202020404040404040404040408080
order1222225510101010101044101010102244444488202020202020202044481010101020202020202020202020202020204040404040404040444224444448848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-11-1-111-111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-111111-1-1
χ6111111111111111111111-11-1-111-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-111
χ7111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-11-1-1-1-111
χ8111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-111-11111-1-1
χ911111111111111111111-11-11-111-1-1-1-1-1-1-1111111-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11-1-111-1-1-11
χ1011111111111111111111-11-11-111-1-1-1-1-1-1-11111-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1111-1
χ1111111111111111111111-11-11-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11-1-1-1-1111-1
χ1211111111111111111111-11-11-1-1-1-111-1-1-1-11111-1-11-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-11111-1-1-11
χ1311111111111111111111-1-1-1-11111-1-111111111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-11-111-1-11-1
χ1411111111111111111111-1-1-1-11111-1-111111111-1-11-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-111-11-1-111-11
χ1511111111111111111111-1-1-1-11-1-11111111111111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-11-1-1-111-11
χ1611111111111111111111-1-1-1-11-1-111111111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-111-1111-1-11-1
χ1722222222222222-2-222220000200-2002222-2-2-2-222000000-2-2000000000000000000002-2-20200-20000000
χ1822222222222222-2-222220000200-2002222-2-2-2-2-2-2000000-2-200000000000000000000-2220-20020000000
χ1922222222222222-2-222220000-200200-2-2-2-2-2-2-2-22200000022000000000000000000002-2-20-20020000000
χ2022222222222222-2-222220000-200200-2-2-2-2-2-2-2-2-2-20000002200000000000000000000-2220200-20000000
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+52−1−5222222-2-22-2-2−1+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+52−1−52−1+52−1−52−1+52−1−521−521−521+521+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+52−1−522-22-2-222-2221−521−521+521+52−1+52−1+52−1−52−1−5200-2-2−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−522-22-2-2-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−520022−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521−521+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+52−1−52-22-22-222-2-2-21−521−521+521+52−1+52−1+52−1−52−1−5200-221−521+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+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+52−1−52-22-22-2-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−52002-21−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521−521+521+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+52−1−52-2-2-2-22222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002-21−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+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+5222222-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+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+522-22-2-222-2221+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+521+521−52−1−52−1−52−1+52−1+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+522-22-2-2-2-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+520022−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521+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+52-22-22-222-2-2-21+521+521−521−52−1−52−1−52−1+52−1+5200-221+521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+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+52-22-22-2-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+52002-21+521−52−1−52−1+521+521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+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+52-2-2-2-22222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002-21+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+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
χ372222-2-2222222222-2-2-2-2-2020-200000000002-22-2220000220000-2-20000000000000000-22-2-200200000000
χ382222-2-2222222222-2-2-2-2-2020-200000000002-22-2-2-20000220000-2-200000000000000002-22200-200000000
χ392222-2-2222222222-2-2-2-2-20-20200000000002-22-2220000-2-20000220000000000000000-22-2200-200000000
χ402222-2-2222222222-2-2-2-2-20-20200000000002-22-2-2-20000-2-200002200000000000000002-22-200200000000
χ412222-2-222222222-22-2-2-2-220-200000000000-22-222200220000-2-2000000000000000000-2-2200200-2000000
χ422222-2-222222222-22-2-2-2-220-200000000000-22-22-2-200220000-2-200000000000000000022-200-2002000000
χ432222-2-222222222-22-2-2-2-2-20200000000000-22-222200-2-2000022000000000000000000-2-2200-2002000000
χ442222-2-222222222-22-2-2-2-2-20200000000000-22-22-2-200-2-200002200000000000000000022-200200-2000000
χ45444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−50000400-400−1+5−1+5−1−5−1−51−51−51+51+5000000001−51+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+5−1−50000-4004001−51−51+51+51−51−51+51+500000000−1+5−1−500000000000000000000000000000000000
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+50000400-400−1−5−1−5−1+5−1+51+51+51−51−5000000001+51−500000000000000000000000000000000000
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+50000-4004001+51+51−51−51+51+51−51−500000000−1−5−1+500000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54-41−51+51−51+5040-40000000000−1+51−5−1−51+5000000−1+5−1−500001−51+50000000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54-41−51+51−51+50-4040000000000−1+51−5−1−51+50000001−51+50000−1+5−1−50000000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-441−51+51−51+540-4000000000001−5−1+51+5−1−50000−1+5−1−500001−51+5000000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-441−51+51−51+5-404000000000001−5−1+51+5−1−500001−51+50000−1+5−1−5000000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54-41+51−51+51−5040-40000000000−1−51+5−1+51−5000000−1−5−1+500001+51−50000000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54-41+51−51+51−50-4040000000000−1−51+5−1+51−50000001+51−50000−1−5−1+50000000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-441+51−51+51−540-4000000000001+5−1−51−5−1+50000−1−5−1+500001+51−5000000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-441+51−51+51−5-404000000000001+5−1−51−5−1+500001+51−50000−1−5−1+5000000000000000000000000000000000
χ5744-4-44-444-4-4-4-4440044-4-4000000000000000000000000000000000000000000000000000000000002i2−2i200
χ5844-4-44-444-4-4-4-4440044-4-400000000000000000000000000000000000000000000000000000000000−2i22i200
χ5944-4-4-4444-4-4-4-44400-4-4440000000022−2200000000000000000000000000000022−2222−220000000000000000000
χ6044-4-4-4444-4-4-4-44400-4-44400000000−2222000000000000000000000000000000−2222−22220000000000000000000
χ6144-4-4-44−1+5−1−51−51+51−51+5−1+5−1−5001−51+5−1+5−1−50000000022−222ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6244-4-4-44−1+5−1−51−51+51−51+5−1+5−1−5001−51+5−1+5−1−50000000022−22−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ6344-4-4-44−1+5−1−51−51+51−51+5−1+5−1−5001−51+5−1+5−1−500000000−22222ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ6444-4-4-44−1+5−1−51−51+51−51+5−1+5−1−5001−51+5−1+5−1−500000000−2222−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6544-4-4-44−1−5−1+51+51−51+51−5−1−5−1+5001+51−5−1−5−1+50000000022−22−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000ζ21+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
χ6644-4-4-44−1−5−1+51+51−51+51−5−1−5−1+5001+51−5−1−5−1+50000000022−222ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000ζ21+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
χ6744-4-4-44−1−5−1+51+51−51+51−5−1−5−1+5001+51−5−1−5−1+500000000−2222−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000−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
χ6844-4-4-44−1−5−1+51+51−51+51−5−1−5−1+5001+51−5−1−5−1+500000000−22222ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000−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
χ694-4-440044-4-444-4-4000000000002i−2i000000000004i−4i0000000000002i−2i2i−2i0000000000000000000002-20000
χ704-4-440044-4-444-4-4000000000002i−2i00000000000−4i4i0000000000002i−2i2i−2i000000000000000000000-220000
χ714-4-440044-4-444-4-400000000000−2i2i000000000004i−4i000000000000−2i2i−2i2i000000000000000000000-220000
χ724-4-440044-4-444-4-400000000000−2i2i00000000000−4i4i000000000000−2i2i−2i2i0000000000000000000002-20000
χ7388-8-88-8−2+25−2−252−252+252−252+25−2+25−2−2500−2+25−2−252−252+25000000000000000000000000000000000000000000000000000000000000000
χ7488-8-88-8−2−25−2+252+252−252+252−25−2−25−2+2500−2−25−2+252+252−25000000000000000000000000000000000000000000000000000000000000000
χ758-88-8008888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000
χ768-88-800−2+25−2−25−2+25−2−252−252+252−252+250000000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ778-88-800−2+25−2−25−2+25−2−252−252+252−252+25000000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ788-88-800−2−25−2+25−2−25−2+252+252−252+252−25000000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ798-88-800−2−25−2+25−2−25−2+252+252−252+252−250000000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000
χ808-8-8800−2+25−2−252−252+25−2+25−2−252−252+25000000000004i−4i0000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000
χ818-8-8800−2+25−2−252−252+25−2+25−2−252−252+2500000000000−4i4i00000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000
χ828-8-8800−2−25−2+252+252−25−2−25−2+252+252−25000000000004i−4i0000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000
χ838-8-8800−2−25−2+252+252−25−2−25−2+252+252−2500000000000−4i4i00000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000

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