Finite Group Databasebeta

← Group #11772066

Character table — Group #11772066

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122444444444488888888888816161616161616161618181818181836363636363636363672727272144
order12224433666666881212121224242424242424242666666664488884161616161616161688882
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iii1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−i1
χ922222222222222-2-22222-2-2-2-2-2-2-2-200000000022-2-2-2-220000000000000
χ1022222222222222-2-22222-2-2-2-2-2-2-2-2000000000-2-22222-20000000000000
χ112222-2-22222222200-2-2-2-200000000000000000220000-222−2−222−2−200000
χ122222-2-22222222200-2-2-2-200000000000000000220000-2−2−222−2−22200000
χ132222-2-22222222200-2-2-2-200000000000000000-2-200002−i2−i2i2i2i2i2−i2−i200000
χ142222-2-22222222200-2-2-2-200000000000000000-2-200002i2i2−i2−i2−i2−i2i2i200000
χ1522-2-2-2222-2-2-2-2220022-2-2000000000000000000022-2-2000000000−i2i2−i2i20
χ1622-2-2-2222-2-2-2-2220022-2-2000000000000000000022-2-2000000000i2−i2i2−i20
χ1722-2-2-2222-2-2-2-2220022-2-20000000000000000000-2-2220000000002−2−220
χ1822-2-2-2222-2-2-2-2220022-2-20000000000000000000-2-222000000000−222−20
χ192-22-2002222-2-2-2-22−200002222−2−2−2−20000000002-22−22−20−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−ζ4300000
χ202-22-2002222-2-2-2-22−200002222−2−2−2−20000000002-22−22−20ζ25+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+ζ4300000
χ212-22-2002222-2-2-2-22−200002222−2−2−2−2000000000-22−22−220ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700000
χ222-22-2002222-2-2-2-22−200002222−2−2−2−2000000000-22−22−220−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700000
χ232-22-2002222-2-2-2-2−220000−2−2−2−222220000000002-2−22−220ζ11+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−ζ4700000
χ242-22-2002222-2-2-2-2−220000−2−2−2−222220000000002-2−22−220−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+ζ4700000
χ252-22-2002222-2-2-2-2−220000−2−2−2−22222000000000-222−22−20−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300000
χ262-22-2002222-2-2-2-2−220000−2−2−2−22222000000000-222−22−20ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000
χ274444441-21-21-21-2441-21-211-2-211-2-241111-2-2-2-200000000000000000000
χ284444441-21-21-21-2441-21-211-2-211-2-2-4-1-1-1-1222200000000000000000000
χ294444441-21-21-21-2-4-41-21-2-1-122-1-122033-3-3000000000000000000000000
χ304444441-21-21-21-2-4-41-21-2-1-122-1-1220-3-333000000000000000000000000
χ31444444-21-21-21-2144-21-21-2-211-2-2114-2-2-2-2111100000000000000000000
χ32444444-21-21-21-2144-21-21-2-211-2-211-42222-1-1-1-100000000000000000000
χ33444444-21-21-21-21-4-4-21-2122-1-122-1-10000033-3-300000000000000000000
χ34444444-21-21-21-21-4-4-21-2122-1-122-1-100000-3-33300000000000000000000
χ3544-4-44-41-2-12-121-200-121-23-3003-3000−i3i3−i3i300−2i32i300000000000000000000
χ3644-4-44-41-2-12-121-200-121-23-3003-3000i3−i3i3−i3002i3−2i300000000000000000000
χ3744-4-44-41-2-12-121-200-121-2-3300-33000−i3i3i3−i3−2i32i30000000000000000000000
χ3844-4-44-41-2-12-121-200-121-2-3300-33000i3−i3−i3i32i3−2i30000000000000000000000
χ3944-4-44-444-4-4-4-44400-4-4440000000000000000000000000000000000000
χ4044-4-44-4-212-12-1-21002-1-21003-3003-3000−2i32i3−i3i3i3−i300000000000000000000
χ4144-4-44-4-212-12-1-21002-1-21003-3003-30002i3−2i3i3−i3−i3i300000000000000000000
χ4244-4-44-4-212-12-1-21002-1-2100-3300-330−2i32i300i3−i3i3−i300000000000000000000
χ4344-4-44-4-212-12-1-21002-1-2100-3300-3302i3−2i300−i3i3−i3i300000000000000000000
χ444-4-440044-4-444-4-4000000000000000000000000022−22−222200000000000000
χ454-4-440044-4-444-4-40000000000000000000000000−222222−2200000000000000
χ468888-8-82-42-42-42-400-24-240000000000000000000000000000000000000
χ478888-8-8-42-42-42-42004-24-20000000000000000000000000000000000000
χ4888-8-8-882-4-24-242-4002-4-240000000000000000000000000000000000000
χ4988-8-8-88-424-24-2-4200-424-20000000000000000000000000000000000000
χ508-88-8002-42-4-24-2442−42000022−22−22−2−2222200000000000000000000000000000
χ518-88-8002-42-4-24-24−42420000−2−2222222−22−2200000000000000000000000000000
χ528-88-800-42-424-24-242−420000−22−22222222−2−200000000000000000000000000000
χ538-88-800-42-424-24-2−424200002222−2−2−22−222200000000000000000000000000000
χ548-8-88002-4-242-4-2400000032−3200−32320000000000000000000000000000000
χ558-8-88002-4-242-4-24000000−32320032−320000000000000000000000000000000
χ568-8-8800-424-2-424-20000000032−3200−323200000000000000000000000000000
χ578-8-8800-424-2-424-200000000−32320032−3200000000000000000000000000000

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