Finite Group Databasebeta

← Group #11799649

Character table — Group #11799649

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11112244444444448888888888881818181818182424242436363636363636363648484848484848484848
order12224433666666881212121224242424242424244488882244416161616161616164466121212121212
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111
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
χ611111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1111-1-1-1-111
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
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-1-1-11111-1-1
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
χ1522-2-2-2222-222-2-2-20022-2-2000000000022-2-22-200000000000002-2000000
χ1622-2-2-2222-222-2-2-20022-2-2000000000022-2-2-220000000000000-22000000
χ1722-2-2-2222-222-2-2-20022-2-20000000000-2-222002i−2i00000000000002i−2i0000
χ1822-2-2-2222-222-2-2-20022-2-20000000000-2-22200−2i2i0000000000000−2i2i0000
χ192-22-200222-2-22-2-2−i2i20000−i2−i2−i2−i2i2i2i2i22i−2i2−22−200000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000
χ202-22-200222-2-22-2-2−i2i20000−i2−i2−i2−i2i2i2i2i22i−2i2−22−200000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000
χ212-22-200222-2-22-2-2−i2i20000−i2−i2−i2−i2i2i2i2i2−2i2i−22−2200000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000
χ222-22-200222-2-22-2-2−i2i20000−i2−i2−i2−i2i2i2i2i2−2i2i−22−2200000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000
χ232-22-200222-2-22-2-2i2−i20000i2i2i2i2−i2−i2−i2−i22i−2i−22−2200000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000000000
χ242-22-200222-2-22-2-2i2−i20000i2i2i2i2−i2−i2−i2−i22i−2i−22−2200000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000000000
χ252-22-200222-2-22-2-2i2−i20000i2i2i2i2−i2−i2−i2−i2−2i2i2−22−200000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000000000
χ262-22-200222-2-22-2-2i2−i20000i2i2i2i2−i2−i2−i2−i2−2i2i2−22−200000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000000000
χ274444441-2-21-211-2441-21-211-2-211-2-20000000000000000000220000-1-1-1-1
χ284444441-2-21-211-2441-21-211-2-211-2-20000000000000000000-2-200001111
χ294444441-2-21-211-2-4-41-21-2-1-122-1-12200000000000000000002-20000-1-111
χ304444441-2-21-211-2-4-41-21-2-1-122-1-1220000000000000000000-22000011-1-1
χ31444444-211-21-2-2144-21-21-2-211-2-211000000222200000000000-1-1-1-10000
χ32444444-211-21-2-2144-21-21-2-211-2-211000000-2-2-2-20000000000011110000
χ33444444-211-21-2-21-4-4-21-2122-1-122-1-100000022-2-200000000000-1-1110000
χ34444444-211-21-2-21-4-4-21-2122-1-122-1-1000000-2-2220000000000011-1-10000
χ3544-4-44-41-221-2-1-1200-121-23-3003-30000000000000000000000000003−33−3
χ3644-4-44-41-221-2-1-1200-121-23-3003-3000000000000000000000000000−33−33
χ3744-4-44-41-221-2-1-1200-121-2-3300-330000000000000000000000000003−3−33
χ3844-4-44-41-221-2-1-1200-121-2-3300-33000000000000000000000000000−333−3
χ3944-4-44-444-444-4-4-400-4-4440000000000000000000000000000000000000
χ4044-4-4-44-21-1-2122-100-212-1003i−3i003i−3i0000002-22i−2i00000000000-11−ii0000
χ4144-4-4-44-21-1-2122-100-212-1003i−3i003i−3i000000-22−2i2i000000000001-1i−i0000
χ4244-4-4-44-21-1-2122-100-212-100−3i3i00−3i3i0000002-2−2i2i00000000000-11i−i0000
χ4344-4-4-44-21-1-2122-100-212-100−3i3i00−3i3i000000-222i−2i000000000001-1−ii0000
χ444-4-440044-4-4-4-444000000000000000022−22−222200000000000000000000000
χ454-4-440044-4-4-4-4440000000000000000−222222−2200000000000000000000000
χ468888-8-82-4-42-422-400-24-240000000000000000000000000000000000000
χ478888-8-8-422-42-4-42004-24-20000000000000000000000000000000000000
χ4888-8-88-8-42-2-4244-2004-2-420000000000000000000000000000000000000
χ4988-8-8-882-442-4-2-24002-4-240000000000000000000000000000000000000
χ508-88-8002-4-4-242-24−4i24i20000−i2−i22i22i2i2i2−2i2−2i200000000000000000000000000000
χ518-88-8002-4-4-242-244i2−4i20000i2i2−2i2−2i2−i2−i22i22i200000000000000000000000000000
χ528-88-800-4224-2-44-2−4i24i200002i22i2−i2−i2−2i2−2i2i2i200000000000000000000000000000
χ538-88-800-4224-2-44-24i2−4i20000−2i2−2i2i2i22i22i2−i2−i200000000000000000000000000000
χ548-8-88002-44-24-22-4000000−3i23i2003i2−3i20000000000000000000000000000000
χ558-8-88002-44-24-22-40000003i2−3i200−3i23i20000000000000000000000000000000
χ568-8-8800-42-24-24-420000000032−3200−323200000000000000000000000000000
χ578-8-8800-42-24-24-4200000000−32320032−3200000000000000000000000000000

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