Finite Group Databasebeta

← Group #12072012

Character table — Group #12072012

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222222244444444888888888888888881010101016161616161616161616161616161616161616161616161616161616202020204040404040404040408080
order1222225510101010101044441010101022444444420202020202020202222881010101020202020202020202020202020204040404040404040444444444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111111111-1-1
χ911111111111111-1-11111111-11-1-111-1-1-1-1-1-1111111111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-11-1
χ1011111111111111-1-11111111-11-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-11
χ1111111111111111-1-11111111-11-1-1-1-111-1-1-1-111111111-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-1-1-1-111-11
χ1211111111111111-1-11111111-11-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-1-11111-1-11-1
χ1311111111111111-1-1111111-11-11-111-1-1-1-1-1-111111111-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-11
χ1411111111111111-1-1111111-11-11-111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1111-1
χ1511111111111111-1-1111111-11-11-1-1-111-1-1-1-1111111111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1111111-11-11-1-1-111-1-1-1-11111-1-1-1-11-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111-1-111-1-1-11
χ172222222222222222-2-222220000-200002222-2-2-2-22222000000-2-200000000000000000000-2-2-2-220000000000
χ182222222222222222-2-222220000-200002222-2-2-2-2-2-2-2-2000000-2-2000000000000000000002222-20000000000
χ1922222222222222-2-2-2-22222000020000-2-2-2-2-2-2-2-222220000002200000000000000000000-2-222-20000000000
χ2022222222222222-2-2-2-22222000020000-2-2-2-2-2-2-2-2-2-2-2-2000000220000000000000000000022-2-220000000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000022−1+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+52−1−5222222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-2−1+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+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-21−521+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
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-22-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000221−521+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+52−1−522-22-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−5200002-2−1+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
χ26222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-22-2-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−520000-22−1+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
χ27222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-222-2-21−521−521+521+52−1+52−1+52−1−52−1−520000-221−521+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
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−5200002-21−521+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
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000022−1−52−1+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+5222222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-2−1−52−1+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+522222−1−52−1+52−1−52−1+52-2-2-2-222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-21+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
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52-2-2-2-22-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000221+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+522-22-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+5200002-2−1−52−1+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
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+522-22-2-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+520000-22−1−52−1+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
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+52-22-22-222-2-21+521+521−521−52−1−52−1−52−1+52−1+520000-221+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
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+52-22-22-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+5200002-21+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
χ372222-2-222222222002-2-2-2-2-2020-20000000002-22-222-2-200002200000000-2-20000000000002-2000002-2000000
χ382222-2-222222222002-2-2-2-2-2020-20000000002-22-2-2-22200002200000000-2-2000000000000-2200000-22000000
χ392222-2-222222222002-2-2-2-2-20-2020000000002-22-222-2-20000-2-200000000220000000000002-200000-22000000
χ402222-2-222222222002-2-2-2-2-20-2020000000002-22-2-2-2220000-2-20000000022000000000000-22000002-2000000
χ412222-2-22222222200-22-2-2-2-220-20000000000-22-2222-2-2002200000000-2-200000000000000-220002-200000000
χ422222-2-22222222200-22-2-2-2-220-20000000000-22-22-2-222002200000000-2-2000000000000002-2000-2200000000
χ432222-2-22222222200-22-2-2-2-2-2020000000000-22-2222-2-200-2-2000000002200000000000000-22000-2200000000
χ442222-2-22222222200-22-2-2-2-2-2020000000000-22-22-2-22200-2-20000000022000000000000002-20002-200000000
χ45444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−544-4-4−1+5−1−5−1+5−1−50000-40000−1+5−1+5−1−5−1−51−51−51+51+500000000001−51+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+5−1−50000400001−51−51+51+51−51−51+51+50000000000−1+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+50000-40000−1−5−1−5−1+5−1+51+51+51−51−500000000001+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+50000400001+51+51−51−51+51+51−51−50000000000−1−5−1+500000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+5040-4000000000−1+51−5−1−51+500000000−1+5−1−5000000001−51+5000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+50-404000000000−1+51−5−1−51+5000000001−51+500000000−1+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+540-400000000001−5−1+51+5−1−5000000−1+5−1−5000000001−51+500000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+51−51+5-40400000000001−5−1+51+5−1−50000001−51+500000000−1+5−1−500000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−5040-4000000000−1−51+5−1+51−500000000−1−5−1+5000000001+51−5000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−50-404000000000−1−51+5−1+51−5000000001+51−500000000−1−5−1+5000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−540-400000000001+5−1−51−5−1+5000000−1−5−1+5000000001+51−500000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−5-40400000000001+5−1−51−5−1+50000001+51−500000000−1−5−1+500000000000000000000000000000
χ5744-4-44-444-4-4-4-4444-40044-4-40000000004-44-4000000000000000000000000000000000000000000000000000
χ5844-4-44-444-4-4-4-444-440044-4-4000000000-44-44000000000000000000000000000000000000000000000000000
χ5944-4-44-4−1+5−1−51−51−51+51+5−1+5−1−54-400−1+5−1−51−51+5000000000−1+51−5−1−51+50000000000000000000000000000ζ7−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
χ6044-4-44-4−1+5−1−51−51−51+51+5−1+5−1−54-400−1+5−1−51−51+5000000000−1+51−5−1−51+50000000000000000000000000000−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
χ6144-4-44-4−1+5−1−51−51−51+51+5−1+5−1−5-4400−1+5−1−51−51+50000000001−5−1+51+5−1−50000000000000000000000000000ζ7−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
χ6244-4-44-4−1+5−1−51−51−51+51+5−1+5−1−5-4400−1+5−1−51−51+50000000001−5−1+51+5−1−50000000000000000000000000000−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
χ6344-4-44-4−1−5−1+51+51+51−51−5−1−5−1+54-400−1−5−1+51+51−5000000000−1−51+5−1+51−50000000000000000000000000000−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
χ6444-4-44-4−1−5−1+51+51+51−51−5−1−5−1+54-400−1−5−1+51+51−5000000000−1−51+5−1+51−50000000000000000000000000000ζ21−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
χ6544-4-44-4−1−5−1+51+51+51−51−5−1−5−1+5-4400−1−5−1+51+51−50000000001+5−1−51−5−1+50000000000000000000000000000−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
χ6644-4-44-4−1−5−1+51+51+51−51−5−1−5−1+5-4400−1−5−1+51+51−50000000001+5−1−51−5−1+50000000000000000000000000000ζ21−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
χ6744-4-4-4444-4-4-4-4440000-4-4440000000000000000000000000000000000000000000000000004i−4i00000000000
χ6844-4-4-4444-4-4-4-4440000-4-444000000000000000000000000000000000000000000000000000−4i4i00000000000
χ694-44-400444-44-4-4-400000000000002i−2i0000000000004-4000000002i−2i2i−2i00000000000000000000000002i−2i0000
χ704-44-400444-44-4-4-400000000000002i−2i000000000000-44000000002i−2i2i−2i0000000000000000000000000−2i2i0000
χ714-44-400444-44-4-4-40000000000000−2i2i0000000000004-400000000−2i2i−2i2i0000000000000000000000000−2i2i0000
χ724-44-400444-44-4-4-40000000000000−2i2i000000000000-4400000000−2i2i−2i2i00000000000000000000000002i−2i0000
χ734-4-440044-44-44-4-40000000000000002i−2i000000004-40000000000000000002i−2i2i−2i00000000000000000002i−2i00
χ744-4-440044-44-44-4-40000000000000002i−2i00000000-440000000000000000002i−2i2i−2i0000000000000000000−2i2i00
χ754-4-440044-44-44-4-4000000000000000−2i2i000000004-4000000000000000000−2i2i−2i2i0000000000000000000−2i2i00
χ764-4-440044-44-44-4-4000000000000000−2i2i00000000-44000000000000000000−2i2i−2i2i00000000000000000002i−2i00
χ7788-8-8-88−2+25−2−252−252−252+252+25−2+25−2−2500002−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-88−2−25−2+252+252+252−252−25−2−25−2+2500002+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000
χ798-88-800−2+25−2−25−2+252−25−2−252+252−252+2500000000000004i−4i0000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000
χ808-88-800−2+25−2−25−2+252−25−2−252+252−252+250000000000000−4i4i00000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000000
χ818-88-800−2−25−2+25−2−252+25−2+252−252+252−2500000000000004i−4i0000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000
χ828-88-800−2−25−2+25−2−252+25−2+252−252+252−250000000000000−4i4i00000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000
χ838-8-8800−2+25−2−252−25−2+252+25−2−252−252+250000000000000004i−4i0000000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000
χ848-8-8800−2+25−2−252−25−2+252+25−2−252−252+25000000000000000−4i4i00000000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000
χ858-8-8800−2−25−2+252+25−2−252−25−2+252+252−250000000000000004i−4i0000000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000
χ868-8-8800−2−25−2+252+25−2−252−25−2+252+252−25000000000000000−4i4i00000000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000

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