Finite Group Databasebeta

← Group #11799793

Character table — Group #11799793

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11112244444444448888888888881818181818182424242436363636363636363648484848484848484848
order12224433666666881212121224242424242424242288884444416161616161616162466121212121212
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1
χ511111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-11-111-1-111-1-1
χ611111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-11-1-11111-1-1
χ711111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-11-1-111-1-111
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-111-1-1-1-111
χ92222222222222222222222222222-2-2-2-2-2-20000-2000000000000000000
χ1022222222222222-2-22222-2-2-2-2-2-2-2-222-2-2-2-200002000000000000000000
χ112222-2-22222222200-2-2-2-2000000002200000000-222−2−222−2−20000000000
χ122222-2-22222222200-2-2-2-2000000002200000000-2−2−222−2−2220000000000
χ132222-2-22222222200-2-2-2-200000000-2-200000000222−2−2−2−2220000000000
χ142222-2-22222222200-2-2-2-200000000-2-2000000002−2−22222−2−20000000000
χ152-22-2-2222-2-222-2-200-2-222000000000022-2-2002i−2i000000000000000002i−2i
χ162-22-2-2222-2-222-2-200-2-222000000000022-2-200−2i2i00000000000000000−2i2i
χ172-22-2-2222-2-222-2-200-2-2220000000000-2-2222i−2i000000000000000002i−2i00
χ182-22-2-2222-2-222-2-200-2-2220000000000-2-222−2i2i00000000000000000−2i2i00
χ192-2-220022-2-2-2-2222−200002222−2−2−2−22-22−22−200000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000
χ202-2-220022-2-2-2-2222−200002222−2−2−2−22-22−22−200000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000
χ212-2-220022-2-2-2-2222−200002222−2−2−2−2-22−22−2200000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000
χ222-2-220022-2-2-2-2222−200002222−2−2−2−2-22−22−2200000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000
χ232-2-220022-2-2-2-222−220000−2−2−2−222222-2−22−2200000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000
χ242-2-220022-2-2-2-222−220000−2−2−2−222222-2−22−2200000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000
χ252-2-220022-2-2-2-222−220000−2−2−2−22222-222−22−200000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000
χ262-2-220022-2-2-2-222−220000−2−2−2−22222-222−22−200000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000
χ274444441-21-21-2-21441-21-211-2-211-2-20000002222000000000000000-1-1-1-1
χ284444441-21-21-2-21441-21-211-2-211-2-2000000-2-2-2-20000000000000001111
χ294444441-21-21-2-21-4-41-21-2-1-122-1-12200000022-2-2000000000000000-1-111
χ304444441-21-21-2-21-4-41-21-2-1-122-1-122000000-2-22200000000000000011-1-1
χ31444444-21-21-211-244-21-21-2-211-2-211000000000000000000022-1-1-1-10000
χ32444444-21-21-211-244-21-21-2-211-2-2110000000000000000000-2-211110000
χ33444444-21-21-211-2-4-4-21-2122-1-122-1-100000000000000000002-2-1-1110000
χ34444444-21-21-211-2-4-4-21-2122-1-122-1-10000000000000000000-2211-1-10000
χ3544-4-4004444-4-4-4-4000000000000000022−22−222200000000000000000000000
χ3644-4-4004444-4-4-4-40000000000000000−222222−2200000000000000000000000
χ374-44-44-444-4-444-4-40044-4-40000000000000000000000000000000000000
χ384-44-44-4-212-1-21-1200-212-1003i−3i003i−3i000000000000000000000−i3i33−30000
χ394-44-44-4-212-1-21-1200-212-1003i−3i003i−3i000000000000000000000i3−i3−330000
χ404-44-44-4-212-1-21-1200-212-100−3i3i00−3i3i000000000000000000000−i3i3−330000
χ414-44-44-4-212-1-21-1200-212-100−3i3i00−3i3i000000000000000000000i3−i33−30000
χ424-44-4-441-2-121-22-100-121-23-3003-3000000002i−2i2i−2i000000000000000−ii−ii
χ434-44-4-441-2-121-22-100-121-23-3003-300000000−2i2i−2i2i000000000000000i−ii−i
χ444-44-4-441-2-121-22-100-121-2-3300-33000000002i−2i−2i2i000000000000000−iii−i
χ454-44-4-441-2-121-22-100-121-2-3300-3300000000−2i2i2i−2i000000000000000i−i−ii
χ468888-8-82-42-42-4-4200-24-240000000000000000000000000000000000000
χ478888-8-8-42-42-422-4004-24-20000000000000000000000000000000000000
χ4888-8-8002-42-4-244-200000032−3200−32320000000000000000000000000000000
χ4988-8-8002-42-4-244-2000000−32320032−320000000000000000000000000000000
χ5088-8-800-42-424-2-2400000000−3i23i2003i2−3i200000000000000000000000000000
χ5188-8-800-42-424-2-24000000003i2−3i200−3i23i200000000000000000000000000000
χ528-88-88-82-4-242-44-2002-4-240000000000000000000000000000000000000
χ538-88-8-88-424-2-42-24004-2-420000000000000000000000000000000000000
χ548-8-88002-4-24-24-4242−42000022−22−22−2−2222200000000000000000000000000000
χ558-8-88002-4-24-24-42−42420000−2−2222222−22−2200000000000000000000000000000
χ568-8-8800-424-24-22-442−420000−22−22222222−2−200000000000000000000000000000
χ578-8-8800-424-24-22-4−424200002222−2−2−22−222200000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.