Finite Group Databasebeta

← Group #12071819

Character table — Group #12071819

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444444488888888888888810101616161616161616161616161616161616161616161616161616161616202020202040404040404040808080
order1222225510101010101044441010101044444442020202020202020444882020202020202020202020202020202020204040404040404040224442224444488
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
χ511111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1
χ611111111111111111111111-1-1-1-11111111111-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ711111111111111111111111-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1
χ911111111111111-1-1111111-11-11-111-1-1-1-1111111-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-11-111-11-1
χ1011111111111111-1-1111111-11-11-111-1-1-1-11111-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-11-11-1-11-11
χ1111111111111111-1-1111111-11-11-1-1-1-1-1-1-11111111-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-11-1-1-11-11
χ1211111111111111-1-1111111-11-11-1-1-1-1-1-1-11111-1-11-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-11-1111-11-1
χ1311111111111111-1-1111111-1-11-1111-1-1-1-1111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1111-1-11
χ1411111111111111-1-1111111-1-11-1111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11111-11-1-1-111-1
χ1511111111111111-1-1111111-1-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-11-1-111-1
χ1611111111111111-1-1111111-1-11-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11111-11-111-1-11
χ172222222222222222-2-22222-20000002222-2-2-2-222000-2-2000000000000000000000000-2-2222-2000000000
χ182222222222222222-2-22222-20000002222-2-2-2-2-2-2000-2-200000000000000000000000022-2-2-22000000000
χ1922222222222222-2-2-2-222222000000-2-2-2-2-2-2-2-22200022000000000000000000000000-2-22-2-22000000000
χ2022222222222222-2-2-2-222222000000-2-2-2-2-2-2-2-2-2-20002200000000000000000000000022-222-2000000000
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+52−1−522-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+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+52−1−522-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-222−1+52−1−521−521−521+521+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+52−1−52-22-22-2221−521−521+521+52−1+52−1+52−1−52−1−5200-22-21−521+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+52−1−52−1−521−521−521+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+52−1−52-22-22-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52002-221−521+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+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+52−1−52-2-22-22221−521−521+521+52−1+52−1+52−1−52−1−5200-2-221−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52-2-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−520022-21−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+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+522-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+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+522-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-222−1−52−1+521+521+521−521−521+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+52-22-22-2221+521+521−521−52−1−52−1−52−1+52−1+5200-22-21+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+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+52-22-22-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52002-221+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+521−521−52−1−52−1−52−1+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+52-2-22-22221+521+521−521−52−1−52−1−52−1+52−1+5200-2-221+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+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+52-2-22-22-2-21+521+521−521−52−1−52−1−52−1+52−1+520022-21+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+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ372222-2-222222222002-2-2-2-2-20020-20000002-22-2220000000002-22-200000000000000002-2-2000020-200000
χ382222-2-222222222002-2-2-2-2-20020-20000002-22-2-2-20000000002-22-20000000000000000-2220000-20200000
χ392222-2-222222222002-2-2-2-2-200-2020000002-22-222000000000-22-2200000000000000002-2-20000-20200000
χ402222-2-222222222002-2-2-2-2-200-2020000002-22-2-2-2000000000-22-220000000000000000-222000020-200000
χ412222-2-22222222200-22-2-2-2-2020-20000000-22-2222000002-22-200000000000000000000-22-200020-2000000
χ422222-2-22222222200-22-2-2-2-2020-20000000-22-22-2-2000002-22-2000000000000000000002-22000-202000000
χ432222-2-22222222200-22-2-2-2-20-2020000000-22-222200000-22-2200000000000000000000-22-2000-202000000
χ442222-2-22222222200-22-2-2-2-20-2020000000-22-22-2-200000-22-22000000000000000000002-2200020-2000000
χ45444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544-4-4−1+5−1−5−1+5−1−5-4000000−1+5−1+5−1−5−1−51−51−51+51+5000001−51+5000000000000000000000000000000000000000
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+5−1−540000001−51−51+51+51−51−51+51+500000−1+5−1−5000000000000000000000000000000000000000
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+5-4000000−1−5−1−5−1+5−1+51+51+51−51−5000001+51−5000000000000000000000000000000000000000
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+540000001+51+51−51−51+51+51−51−500000−1−5−1+5000000000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-41−51+51−51+50040-4000000−1+51−5−1−51+500000000000−1+51−5−1−51+50000000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-41−51+51−51+500-404000000−1+51−5−1−51+5000000000001−5−1+51+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+5040-400000001−5−1+51+5−1−50000000−1+51−5−1−51+500000000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-441−51+51−51+50-40400000001−5−1+51+5−1−500000001−5−1+51+5−1−500000000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−50040-4000000−1−51+5−1+51−500000000000−1−51+5−1+51−50000000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−500-404000000−1−51+5−1+51−5000000000001+5−1−51−5−1+50000000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−5040-400000001+5−1−51−5−1+50000000−1−51+5−1+51−500000000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−50-40400000001+5−1−51−5−1+500000001+5−1−51−5−1+500000000000000000000000000000000000
χ5744-4-40044-4-44-44-400000000000002i−2i000000004-400000000000002i−2i2i−2i00000000000000000000002i−2i000
χ5844-4-40044-4-44-44-400000000000002i−2i00000000-4400000000000002i−2i2i−2i0000000000000000000000−2i2i000
χ5944-4-40044-4-44-44-40000000000000−2i2i000000004-40000000000000−2i2i−2i2i0000000000000000000000−2i2i000
χ6044-4-40044-4-44-44-40000000000000−2i2i00000000-440000000000000−2i2i−2i2i00000000000000000000002i−2i000
χ614-44-44-44444-4-4-4-44-40044-4-400000004-44-400000000000000000000000000000000000000000000000000
χ624-44-44-44444-4-4-4-4-440044-4-40000000-44-4400000000000000000000000000000000000000000000000000
χ634-44-44-4−1+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
χ644-44-44-4−1+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
χ654-44-44-4−1+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
χ664-44-44-4−1+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
χ674-44-44-4−1−5−1+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
χ684-44-44-4−1−5−1+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
χ694-44-44-4−1−5−1+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
χ704-44-44-4−1−5−1+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
χ714-44-4-444444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000004i−4i0000000000
χ724-44-4-444444-4-4-4-40000-4-4440000000000000000000000000000000000000000000000000−4i4i0000000000
χ7388-8-800−2+25−2−252−252+25−2+252−25−2−252+2500000000000004i−4i00000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000
χ7488-8-800−2+25−2−252−252+25−2+252−25−2−252+250000000000000−4i4i000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000
χ7588-8-800−2−25−2+252+252−25−2−252+25−2+252−2500000000000004i−4i00000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000
χ7688-8-800−2−25−2+252+252−25−2−252+25−2+252−250000000000000−4i4i000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000
χ778-88-8-88−2+25−2−25−2+25−2−252−252−252+252+2500002−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000
χ788-88-8-88−2−25−2+25−2−25−2+252+252+252−252−2500002+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000
χ798-8-880088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ818-8-8800−2+25−2−252−252+252−25−2+252+25−2−250000000000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ828-8-8800−2−25−2+252+252−252+25−2−252−25−2+250000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ838-8-8800−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000

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