Finite Group Databasebeta

← Group #12072839

Character table — Group #12072839

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444448888888888888888888810101010161616161616161616161616161616161616161616161616161616202040404040404040404040404080
order1222225510101010101044101010102244444444882020202020202020224481010101020202020202020202020202020204040404040404040242444444444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111-11-1-1-111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-11-111-1-1-1-11
χ6111111111111111111111-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-111-11-1-11111-1
χ7111111111111111111111-11-1-1-1-1-11111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-11-1-1-11111-1
χ8111111111111111111111-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1111-1-1-1-11
χ911111111111111111111-11-11-1-11111-1-1111111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1
χ1011111111111111111111-11-11-1-11111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1111
χ1111111111111111111111-11-11-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-1111
χ1211111111111111111111-11-11-1-1-1-1-1-11111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11111111-1-1-1
χ1311111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11-1111-1-111-1
χ1411111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-111-1-11
χ1511111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-11-11-1-111-1-11
χ1611111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-11-111-1-111-1
χ1722222222222222-2-22222020-200000000-2-2-2-2-2-2-2-222-2-20002200000000000000000000002-2-2020000000000
χ1822222222222222-2-22222020-200000000-2-2-2-2-2-2-2-2-2-222000220000000000000000000000-2220-20000000000
χ1922222222222222-2-222220-202000000002222-2-2-2-222-2-2000-2-200000000000000000000002-220-20000000000
χ2022222222222222-2-222220-202000000002222-2-2-2-2-2-222000-2-20000000000000000000000-22-2020000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52222222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200002−1+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+52−1−52222222-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2−1+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+52−1−522-22-2-2-222-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−5200002−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522-22-2-2-2-2-222221−521−521+521+52−1+52−1+52−1−52−1−520000-2−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52-22-22-2-22222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-21−521+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+521−521−521+521+52000000000000000
χ26222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-22-22-2-2-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000021−521+52−1+52−1−521−521+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
χ27222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-2-2-22222-2-2221−521−521+521+52−1+52−1+52−1−52−1−520000-21−521+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+52−1−5222−1+52−1−52−1+52−1−52-2-2-2-222-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−52000021−521+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+5222−1−52−1+52−1−52−1+52222222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200002−1−52−1+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+52222222-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2−1−52−1+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+522-22-2-2-222-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+5200002−1−52−1+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+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+522-22-2-2-2-2-222221+521+521−521−52−1−52−1−52−1+52−1+520000-2−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+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+52-22-22-2-22222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-21+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+521−521−521+521+521−521−52000000000000000
χ34222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-22-22-2-2-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000021+521−52−1−52−1+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
χ35222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-2-2-22222-2-2221+521+521−521−52−1−52−1−52−1+52−1+520000-21+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+5222−1−52−1+52−1−52−1+52-2-2-2-222-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+52000021+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
χ372222-2-2222222222-2-2-2-2-200002-200000000002-22-22222000000022-2-20000000000000000-2-200020-20000000
χ382222-2-2222222222-2-2-2-2-200002-200000000002-22-2-2-2-2-2000000022-2-2000000000000000022000-2020000000
χ392222-2-2222222222-2-2-2-2-20000-2200000000002-22-222220000000-2-2220000000000000000-2-2000-2020000000
χ402222-2-2222222222-2-2-2-2-20000-2200000000002-22-2-2-2-2-20000000-2-22200000000000000002200020-20000000
χ412222-2-222222222-22-2-2-2-220-20000000000000-22-2222-2-202200-2-200000000000000000000-220200-200000000
χ422222-2-222222222-22-2-2-2-220-20000000000000-22-22-2-22202200-2-2000000000000000000002-20-200200000000
χ432222-2-222222222-22-2-2-2-2-2020000000000000-22-2222-2-20-2-2002200000000000000000000-220-200200000000
χ442222-2-222222222-22-2-2-2-2-2020000000000000-22-22-2-2220-2-20022000000000000000000002-20200-200000000
χ45444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−5040-4000000001−51−51+51+51−51−51+51+50000000−1+5−1−50000000000000000000000000000000000000
χ46444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−50-40400000000−1+5−1+5−1−5−1−51−51−51+51+500000001−51+50000000000000000000000000000000000000
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+5040-4000000001+51+51−51−51+51+51−51−50000000−1−5−1+50000000000000000000000000000000000000
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+50-40400000000−1−5−1−5−1+5−1+51+51+51−51−500000001+51−50000000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54-41−51+51−51+500004-40000000000−1+51−5−1−51+500000000000−1+5−1−51−51+50000000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54-41−51+51−51+50000-440000000000−1+51−5−1−51+5000000000001−51+5−1+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+540-400000000000001−5−1+51+5−1−500000−1+5−1−5001−51+500000000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-441−51+51−51+5-40400000000000001−5−1+51+5−1−5000001−51+500−1+5−1−500000000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54-41+51−51+51−500004-40000000000−1−51+5−1+51−500000000000−1−5−1+51+51−50000000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54-41+51−51+51−50000-440000000000−1−51+5−1+51−5000000000001+51−5−1−5−1+50000000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-441+51−51+51−540-400000000000001+5−1−51−5−1+500000−1−5−1+5001+51−500000000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-441+51−51+51−5-40400000000000001+5−1−51−5−1+5000001+51−500−1−5−1+500000000000000000000000000000000000
χ5744-4-44-44444-4-4-4-400-4-444000000000022−220000000000000000000000000000000000022−2222−22000000000000000
χ5844-4-44-44444-4-4-4-400-4-4440000000000−222200000000000000000000000000000000000−2222−2222000000000000000
χ5944-4-44-4−1+5−1−5−1+5−1−51−51+51−51+5001−51+5−1+5−1−5000000000022−22−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000ζ7−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
χ6044-4-44-4−1+5−1−5−1+5−1−51−51+51−51+5001−51+5−1+5−1−5000000000022−222ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000−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+5−1−5−1+5−1−51−51+51−51+5001−51+5−1+5−1−50000000000−2222−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000−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
χ6244-4-44-4−1+5−1−5−1+5−1−51−51+51−51+5001−51+5−1+5−1−50000000000−22222ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000ζ7−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
χ6344-4-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+51−5−1−5−1+5000000000022−222ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ6444-4-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+51−5−1−5−1+5000000000022−22−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ6544-4-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+51−5−1−5−1+50000000000−22222ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ6644-4-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+51−5−1−5−1+50000000000−2222−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ6744-4-4-444444-4-4-4-40044-4-400000000000000000000000000000000000000000000000000000000000000022−220
χ6844-4-4-444444-4-4-4-40044-4-4000000000000000000000000000000000000000000000000000000000000000−22220
χ694-44-40044-4-444-4-4000000000000002i−2i00000000004-4000000000000000002i−2i2i−2i0000000000000000002i−2i000
χ704-44-40044-4-444-4-4000000000000002i−2i0000000000-44000000000000000002i−2i2i−2i000000000000000000−2i2i000
χ714-44-40044-4-444-4-400000000000000−2i2i00000000004-400000000000000000−2i2i−2i2i000000000000000000−2i2i000
χ724-44-40044-4-444-4-400000000000000−2i2i0000000000-4400000000000000000−2i2i−2i2i0000000000000000002i−2i000
χ734-4-440044-4-4-4-4440000000000002-2000000000000004-4000000000002-22-2000000000000000000002-200000
χ744-4-440044-4-4-4-4440000000000002-200000000000000-44000000000002-22-200000000000000000000-2200000
χ754-4-440044-4-4-4-444000000000000-22000000000000004-400000000000-22-2200000000000000000000-2200000
χ764-4-440044-4-4-4-444000000000000-2200000000000000-4400000000000-22-22000000000000000000002-200000
χ7788-8-8-88−2+25−2−25−2+25−2−252−252+252−252+2500−2+25−2−252−252+25000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-88−2−25−2+25−2−25−2+252+252−252+252−2500−2−25−2+252+252−25000000000000000000000000000000000000000000000000000000000000000000
χ798-88-800−2+25−2−252−252+25−2+25−2−252−252+25000000000000004i−4i00000000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000
χ808-88-800−2+25−2−252−252+25−2+25−2−252−252+2500000000000000−4i4i000000000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000
χ818-88-800−2−25−2+252+252−25−2−25−2+252+252−25000000000000004i−4i00000000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000
χ828-88-800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000−4i4i000000000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000
χ838-8-8800−2+25−2−252−252+252−252+25−2+25−2−250000000000004-4000000000000000000000000000−1+51−5−1−51+5000000000000000000000000000
χ848-8-8800−2+25−2−252−252+252−252+25−2+25−2−25000000000000-440000000000000000000000000001−5−1+51+5−1−5000000000000000000000000000
χ858-8-8800−2−25−2+252+252−252+252−25−2−25−2+250000000000004-4000000000000000000000000000−1−51+5−1+51−5000000000000000000000000000
χ868-8-8800−2−25−2+252+252−252+252−25−2−25−2+25000000000000-440000000000000000000000000001+5−1−51−5−1+5000000000000000000000000000

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