Finite Group Databasebeta

← Group #11798863

Character table — Group #11798863

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11112244444444448888888888881818181818182424242436363636363636363648484848484848484848
order1222443366666688121212122424242424242424448888224441616161616161616226666661212
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1
χ511111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-11-11111-1-1-1-1
χ611111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1111-1-111-1-1
χ711111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11111-1-1-1-1-11-1-1-1-11111
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-1-1-111-1-111
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
χ1522-2-2-2222-2-2-222-20022-2-2000000000022-2-2002i−2i000000000000000002i−2i
χ1622-2-2-2222-2-2-222-20022-2-2000000000022-2-200−2i2i00000000000000000−2i2i
χ1722-2-2-2222-2-2-222-20022-2-20000000000-2-2222-200000000000002-2000000
χ1822-2-2-2222-2-2-222-20022-2-20000000000-2-222-220000000000000-22000000
χ192-2-220022-22-2-2-222−200002222−2−2−2−22-22−22−200000−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
χ202-2-220022-22-2-2-222−200002222−2−2−2−22-22−22−200000ζ25−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
χ212-2-220022-22-2-2-222−200002222−2−2−2−2-22−22−2200000ζ11−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
χ222-2-220022-22-2-2-222−200002222−2−2−2−2-22−22−2200000−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
χ232-2-220022-22-2-2-22−220000−2−2−2−222222-2−22−2200000ζ11−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
χ242-2-220022-22-2-2-22−220000−2−2−2−222222-2−22−2200000−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
χ252-2-220022-22-2-2-22−220000−2−2−2−22222-222−22−200000−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
χ262-2-220022-22-2-2-22−220000−2−2−2−22222-222−22−200000ζ25−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
χ274444441-21-2-21-21441-21-211-2-211-2-2000000222200000000000-1-10000-1-1
χ284444441-21-2-21-21441-21-211-2-211-2-2000000-2-2-2-20000000000011000011
χ294444441-21-2-21-21-4-41-21-2-1-122-1-12200000022-2-200000000000-1-1000011
χ304444441-21-2-21-21-4-41-21-2-1-122-1-122000000-2-22200000000000110000-1-1
χ31444444-21-211-21-244-21-21-2-211-2-21100000000000000000002200-1-1-1-100
χ32444444-21-211-21-244-21-21-2-211-2-2110000000000000000000-2-200111100
χ33444444-21-211-21-2-4-4-21-2122-1-122-1-100000000000000000002-200-1-11100
χ34444444-21-211-21-2-4-4-21-2122-1-122-1-10000000000000000000-220011-1-100
χ3544-4-44-444-4-4-444-400-4-4440000000000000000000000000000000000000
χ3644-4-44-4-212-1-1-212002-1-21003-3003-300000000000000000000000−i3i3−i3i300
χ3744-4-44-4-212-1-1-212002-1-21003-3003-300000000000000000000000i3−i3i3−i300
χ3844-4-44-4-212-1-1-212002-1-2100-3300-3300000000000000000000000−i3i3i3−i300
χ3944-4-44-4-212-1-1-212002-1-2100-3300-3300000000000000000000000i3−i3−i3i300
χ4044-4-4-441-2-1221-2-1001-2-123i−3i003i−3i000000002-22i−2i00000000000-110000−ii
χ4144-4-4-441-2-1221-2-1001-2-123i−3i003i−3i00000000-22−2i2i000000000001-10000i−i
χ4244-4-4-441-2-1221-2-1001-2-12−3i3i00−3i3i000000002-2−2i2i00000000000-110000i−i
χ4344-4-4-441-2-1221-2-1001-2-12−3i3i00−3i3i00000000-222i−2i000000000001-10000−ii
χ444-44-400444-44-4-4-4000000000000000022−22−222200000000000000000000000
χ454-44-400444-44-4-4-40000000000000000−222222−2200000000000000000000000
χ468888-8-82-42-4-42-4200-24-240000000000000000000000000000000000000
χ478888-8-8-42-422-42-4004-24-20000000000000000000000000000000000000
χ4888-8-88-82-4-2442-4-200-242-40000000000000000000000000000000000000
χ4988-8-8-88-424-2-2-42400-424-20000000000000000000000000000000000000
χ508-88-8002-424-4-24-2000000−3i23i2003i2−3i20000000000000000000000000000000
χ518-88-8002-424-4-24-20000003i2−3i200−3i23i20000000000000000000000000000000
χ528-88-800-42-4-224-240000000032−3200−323200000000000000000000000000000
χ538-88-800-42-4-224-2400000000−32320032−3200000000000000000000000000000
χ548-8-88002-4-2-44-24242−42000022−22−22−2−2222200000000000000000000000000000
χ558-8-88002-4-2-44-242−42420000−2−2222222−22−2200000000000000000000000000000
χ568-8-8800-4242-24-2-442−420000−22−22222222−2−200000000000000000000000000000
χ578-8-8800-4242-24-2-4−424200002222−2−2−22−222200000000000000000000000000000

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