Finite Group Databasebeta

← Group #12073665

Character table — Group #12073665

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222222444444448888888888888161616161616161616161616161616161616161616161616161616161616202020202020404040404080808080
order1222225510101010101022441010101044444101010102020202024881010101020202020202020202020202020204040404040404040224444222444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1
χ911111111111111-1-1111111-111-1-1-1-1-1-111111-11-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11-11-11-1
χ1011111111111111-1-1111111-111-1-1-1-1-1-111111-11-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-11-11-11-11
χ1111111111111111-1-1111111-111-1-1-1-1-1-11111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-11-11-1-11-11
χ1211111111111111-1-1111111-111-1-1-1-1-1-11111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-11-111-11-1
χ1311111111111111-1-1111111-1-1-111-1-1-1-111111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-11
χ1411111111111111-1-1111111-1-1-111-1-1-1-111111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1
χ1511111111111111-1-1111111-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11-11-111-1
χ1611111111111111-1-1111111-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-11-1-11
χ172222222222222222-2-22222-200002222-2-2-2-200000000-2-20000000000000000000022-2-2-2-2200000000
χ182222222222222222-2-22222-200002222-2-2-2-200000000-2-200000000000000000000-2-22222-200000000
χ1922222222222222-2-2-2-2222220000-2-2-2-2-2-2-2-200000000220000000000000000000022-2-222-200000000
χ2022222222222222-2-2-2-2222220000-2-2-2-2-2-2-2-2000000002200000000000000000000-2-222-2-2200000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+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+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-21−521−521+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+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+52−1−522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2221−521−521+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+52−1−52-222-2-21−521−521+521+52−1+52−1+52−1−52−1−522-22-2−1+52−1+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+52−1−52−1−521−521−521+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+52−1−52-222-2-21−521−521+521+52−1+52−1+52−1−52−1−52-22-221−521−521+521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−522-2-22−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−52-222-21−521−521+521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+5222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+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+5222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-21+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+521−521−521+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+522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+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+522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+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+52-222-2-21+521+521−521−52−1−52−1−52−1+52−1+522-22-2−1−52−1−52−1+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+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+52-222-2-21+521+521−521−52−1−52−1−52−1+52−1+52-22-221+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+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+52-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+522-2-22−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+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+52-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+52-222-21+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+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ372222-2-222222222002-2-2-2-2-20002-200002-22-2000000000000002-22-20000000000002-22-2000020-20000
χ382222-2-222222222002-2-2-2-2-20002-200002-22-2000000000000002-22-2000000000000-22-220000-2020000
χ392222-2-222222222002-2-2-2-2-2000-2200002-22-200000000000000-22-220000000000002-22-20000-2020000
χ402222-2-222222222002-2-2-2-2-2000-2200002-22-200000000000000-22-22000000000000-22-22000020-20000
χ412222-2-22222222200-22-2-2-2-202-2000000-22-2200000000002-22-200000000000000002-2-2200020-200000
χ422222-2-22222222200-22-2-2-2-202-2000000-22-2200000000002-22-20000000000000000-222-2000-20200000
χ432222-2-22222222200-22-2-2-2-20-22000000-22-220000000000-22-2200000000000000002-2-22000-20200000
χ442222-2-22222222200-22-2-2-2-20-22000000-22-220000000000-22-220000000000000000-222-200020-200000
χ45444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544-4-4−1+5−1−5−1+5−1−5-40000−1+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+5−1−5−1−5-4-4-4-4−1+5−1−5−1+5−1−5400001−51−51+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+544-4-4−1−5−1+5−1−5−1+5-40000−1−5−1−5−1+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+5-4-4-4-4−1−5−1+5−1−5−1+5400001+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+5−1−5−1−5004-41−51+51−51+50004-40000−1+51−5−1−51+500000000000000−1+51−5−1−51+5000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-41−51+51−51+5000-440000−1+51−5−1−51+5000000000000001−5−1+51+5−1−5000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-441−51+51−51+504-40000001−5−1+51+5−1−50000000000−1+51−5−1−51+50000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-441−51+51−51+50-440000001−5−1+51+5−1−500000000001−5−1+51+5−1−50000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−50004-40000−1−51+5−1+51−500000000000000−1−51+5−1+51−5000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−5000-440000−1−51+5−1+51−5000000000000001+5−1−51−5−1+5000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−504-40000001+5−1−51−5−1+50000000000−1−51+5−1+51−50000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−50-440000001+5−1−51−5−1+500000000001+5−1−51−5−1+50000000000000000000000000000000
χ574-4-444-44444-4-4-4-4000044-4-4000000000000000000000000000000000000000000000004i−4i000000000
χ584-4-444-44444-4-4-4-4000044-4-400000000000000000000000000000000000000000000000−4i4i000000000
χ594-4-44-444444-4-4-4-44-400-4-444000004-44-40000000000000000000000000000000000000000000000000
χ604-4-44-444444-4-4-4-4-4400-4-44400000-44-440000000000000000000000000000000000000000000000000
χ614-4-44-44−1+5−1−5−1+5−1−51−51−51+51+54-4001−51+5−1+5−1−500000−1+51−5−1−51+500000000000000000000000000ζ7−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
χ624-4-44-44−1+5−1−5−1+5−1−51−51−51+51+54-4001−51+5−1+5−1−500000−1+51−5−1−51+500000000000000000000000000−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
χ634-4-44-44−1+5−1−5−1+5−1−51−51−51+51+5-44001−51+5−1+5−1−5000001−5−1+51+5−1−500000000000000000000000000ζ7−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
χ644-4-44-44−1+5−1−5−1+5−1−51−51−51+51+5-44001−51+5−1+5−1−5000001−5−1+51+5−1−500000000000000000000000000−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
χ654-4-44-44−1−5−1+5−1−5−1+51+51+51−51−54-4001+51−5−1−5−1+500000−1−51+5−1+51−500000000000000000000000000−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
χ664-4-44-44−1−5−1+5−1−5−1+51+51+51−51−54-4001+51−5−1−5−1+500000−1−51+5−1+51−500000000000000000000000000ζ21−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
χ674-4-44-44−1−5−1+5−1−5−1+51+51+51−51−5-44001+51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000000000000−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
χ684-4-44-44−1−5−1+5−1−5−1+51+51+51−51−5-44001+51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000000000000ζ21−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
χ6988-8-80088-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ7088-8-800−2+25−2−252−252+25−2+252−25−2−252+2500000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000000000000000
χ7188-8-800−2+25−2−252−252+25−2+252−25−2−252+250000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000000000000000
χ7288-8-800−2−25−2+252+252−25−2−252+25−2+252−250000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000000000000
χ7388-8-800−2−25−2+252+252−25−2−252+25−2+252−2500000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000000000000000
χ748-88-80088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ758-88-800−2+25−2−252−252+252−25−2+252+25−2−250000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ768-88-800−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ778-88-800−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ788-88-800−2−25−2+252+252−252+25−2−252−25−2+250000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000
χ798-8-888-8−2+25−2−25−2+25−2−252−252−252+252+250000−2+25−2−252−252+250000000000000000000000000000000000000000000000000000000000
χ808-8-888-8−2−25−2+25−2−25−2+252+252+252−252−250000−2−25−2+252+252−250000000000000000000000000000000000000000000000000000000000

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