Finite Group Databasebeta

← Group #12073421

Character table — Group #12073421

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444444488888888888888810101616161616161616161616161616161616161616161616161616161616202020202040404040404040808080
order1222225510101010101022441010101044444441010101020202020224882020202020202020202020202020202020204040404040404040222444444444288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1
χ4111111111111111111111111111-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1111-1-1
χ61111111111111111111111-1-11-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111
χ71111111111111111111111-1-11-1-1-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-111
χ81111111111111111111111-1-11-1-1-1-111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111111-1-1
χ911111111111111-1-11111111-1-11-111-1-1-1-1111111-11-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-11-111-11-1
χ1011111111111111-1-11111111-1-11-111-1-1-1-11111-1-1-11-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-111-11-1-11-11
χ1111111111111111-1-11111111-1-11-1-1-1-1-1-1-11111111-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-1-11-11
χ1211111111111111-1-11111111-1-11-1-1-1-1-1-1-11111-1-11-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1111-11-1
χ1311111111111111-1-1111111-11-1-1111-1-1-1-1111111-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-111-11-1-1111-1-11
χ1411111111111111-1-1111111-11-1-1111-1-1-1-11111-1-1-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-11-111-1-1-111-1
χ1511111111111111-1-1111111-11-1-11-1-1-1-1-1-111111111-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-11-1-11-1-111-1
χ1611111111111111-1-1111111-11-1-11-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-11-111-111-1-11
χ172222222222222222-2-2222200-200002222-2-2-2-2220000000-2-200000000000000000000222-2-200-20000000
χ182222222222222222-2-2222200-200002222-2-2-2-2-2-20000000-2-200000000000000000000-2-2-2220020000000
χ1922222222222222-2-2-2-222220020000-2-2-2-2-2-2-2-222000000022000000000000000000002-2-2-2-20020000000
χ2022222222222222-2-2-2-222220020000-2-2-2-2-2-2-2-2-2-200000002200000000000000000000-2222200-20000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200222−1+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+52−1−5222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2-2−1+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+52−1−522222−1+52−1−52−1+52−1−52-2-22-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002-2-21−521+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
χ24222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2221−521+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
χ25222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-2-22-2221−521−521+521+52−1+52−1+52−1−52−1−5200-22-2−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+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+52−1−522-2-22-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52002-22−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52-22-2-22221−521−521+521+52−1+52−1+52−1−52−1−5200-2-221−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ28222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-2-22-2-21−521−521+521+52−1+52−1+52−1−52−1−520022-21−521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+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+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200222−1−52−1+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+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2-2−1−52−1+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+522222−1−52−1+52−1−52−1+52-2-22-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002-2-21+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
χ32222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2221+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
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+522-2-22-2221+521+521−521−52−1−52−1−52−1+52−1+5200-22-2−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+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+522-2-22-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52002-22−1−52−1+521+521−521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+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+52-22-2-22221+521+521−521−52−1−52−1−52−1+52−1+5200-2-221+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+521+521+521−521−52−1−52−1−52−1+52−1+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+52-22-2-22-2-21+521+521−521−52−1−52−1−52−1+52−1+520022-21+521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ372222-2-222222222002-2-2-2-2-20200-20000002-22-22200000220000-2-20000000000000000-2002-20200-200000
χ382222-2-222222222002-2-2-2-2-20200-20000002-22-2-2-200000220000-2-20000000000000000200-220-200200000
χ392222-2-222222222002-2-2-2-2-20-20020000002-22-22200000-2-20000220000000000000000-2002-20-200200000
χ402222-2-222222222002-2-2-2-2-20-20020000002-22-2-2-200000-2-20000220000000000000000200-220200-200000
χ412222-2-22222222200-22-2-2-2-2200-20000000-22-2222000220000-2-2000000000000000000-200-22200-2000000
χ422222-2-22222222200-22-2-2-2-2200-20000000-22-22-2-2000220000-2-20000000000000000002002-2-2002000000
χ432222-2-22222222200-22-2-2-2-2-20020000000-22-2222000-2-2000022000000000000000000-200-22-2002000000
χ442222-2-22222222200-22-2-2-2-2-20020000000-22-22-2-2000-2-20000220000000000000000002002-2200-2000000
χ45444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-4-4−1+5−1−5−1+5−1−500-40000−1+5−1+5−1−5−1−51−51−51+51+50000000001−51+500000000000000000000000000000000000
χ46444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−500400001−51−51+51+51−51−51+51+5000000000−1+5−1−500000000000000000000000000000000000
χ47444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-4-4−1−5−1+5−1−5−1+500-40000−1−5−1−5−1+5−1+51+51+51−51−50000000001+51−500000000000000000000000000000000000
χ48444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+500400001+51+51−51−51+51+51−51−5000000000−1−5−1+500000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5004-41−51+51−51+50400-4000000−1+51−5−1−51+50000000−1+5−1−500001−51+50000000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5004-41−51+51−51+50-4004000000−1+51−5−1−51+500000001−51+50000−1+5−1−50000000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-441−51+51−51+5400-400000001−5−1+51+5−1−500000−1+5−1−500001−51+5000000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-441−51+51−51+5-400400000001−5−1+51+5−1−5000001−51+50000−1+5−1−5000000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5004-41+51−51+51−50400-4000000−1−51+5−1+51−50000000−1−5−1+500001+51−50000000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5004-41+51−51+51−50-4004000000−1−51+5−1+51−500000001+51−50000−1−5−1+50000000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-441+51−51+51−5400-400000001+5−1−51−5−1+500000−1−5−1+500001+51−5000000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-441+51−51+51−5-400400000001+5−1−51−5−1+5000001+51−50000−1−5−1+5000000000000000000000000000000000
χ5744-4-44-44444-4-4-4-40000-4-444000000000000000000000000000000000000000000000004-4000000000000
χ5844-4-44-44444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000-44000000000000
χ5944-4-4-444444-4-4-4-44-40044-4-400000004-44-400000000000000000000000000000000000000000000000000
χ6044-4-4-444444-4-4-4-4-440044-4-40000000-44-4400000000000000000000000000000000000000000000000000
χ6144-4-4-44−1+5−1−5−1+5−1−51−51+51−51+54-400−1+5−1−51−51+50000000−1+51−5−1−51+5000000000000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6244-4-4-44−1+5−1−5−1+5−1−51−51+51−51+54-400−1+5−1−51−51+50000000−1+51−5−1−51+5000000000000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−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+5−1−5−1+5−1−51−51+51−51+5-4400−1+5−1−51−51+500000001−5−1+51+5−1−5000000000000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+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+5−1−5−1+5−1−51−51+51−51+5-4400−1+5−1−51−51+500000001−5−1+51+5−1−5000000000000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6544-4-4-44−1−5−1+5−1−5−1+51+51−51+51−54-400−1−5−1+51+51−50000000−1−51+5−1+51−5000000000000000000000000000−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
χ6644-4-4-44−1−5−1+5−1−5−1+51+51−51+51−54-400−1−5−1+51+51−50000000−1−51+5−1+51−5000000000000000000000000000ζ21−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
χ6744-4-4-44−1−5−1+5−1−5−1+51+51−51+51−5-4400−1−5−1+51+51−500000001+5−1−51−5−1+5000000000000000000000000000−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
χ6844-4-4-44−1−5−1+5−1−5−1+51+51−51+51−5-4400−1−5−1+51+51−500000001+5−1−51−5−1+5000000000000000000000000000ζ21−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
χ694-4-440044-4-4-4-44400000000000002-2000000004-4000000000000000002-22-20000000000000000002-2000
χ704-4-440044-4-4-4-44400000000000002-200000000-44000000000000000002-22-2000000000000000000-22000
χ714-4-440044-4-4-4-4440000000000000-22000000004-400000000000000000-22-22000000000000000000-22000
χ724-4-440044-4-4-4-4440000000000000-2200000000-4400000000000000000-22-220000000000000000002-2000
χ7388-8-88-8−2+25−2−25−2+25−2−252−252+252−252+2500002−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000
χ7488-8-88-8−2−25−2+25−2−25−2+252+252−252+252−2500002+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000
χ758-88-80088-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000
χ768-88-800−2+25−2−252−252+25−2+25−2−252−252+2500000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ778-88-800−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ788-88-800−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ798-88-800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ808-8-8800−2+25−2−252−252+252−252+25−2+25−2−2500000000000004-4000000000000000000000000000−1+51−5−1−51+500000000000000000000000
χ818-8-8800−2+25−2−252−252+252−252+25−2+25−2−250000000000000-440000000000000000000000000001−5−1+51+5−1−500000000000000000000000
χ828-8-8800−2−25−2+252+252−252+252−25−2−25−2+2500000000000004-4000000000000000000000000000−1−51+5−1+51−500000000000000000000000
χ838-8-8800−2−25−2+252+252−252+252−25−2−25−2+250000000000000-440000000000000000000000000001+5−1−51−5−1+500000000000000000000000

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