Finite Group Databasebeta

← Group #11721565

Character table — Group #11721565

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222223333444446666666666668899999912121212121212121212121212181818181818181818242424242424363636363636
order123468833664412242433366612122424242412124412121212121212121212122424242424242668824242424121212121212226666
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111-1-1111111111111111-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ61111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ71111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ81111111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ91111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ101111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ111111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ121111111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311111-1-111111-11-1-111111111-1-1-1-11-11111111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-11-11-11-11-11-11-1
χ1411111-1-111111-11-1-111111111-1-1-1-11-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-1-1-11111111-11-11-1-11-11-11
χ1511111-1-11111-111-1-111111111-1-1-1-1-11111111-11-11111-1-1-1-1-1-1111-1-1-1-1-1-1-11-11-11-11-11-11
χ1611111-1-11111-111-1-111111111-1-1-1-1-11-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1111111-11-11-111-11-11-1
χ1711111-1-1−1−i32−1+i32−1−i32−1+i321-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-111−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i32
χ1811111-1-1−1−i32−1+i32−1−i32−1+i321-11-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-111+i32−1−i321−i32−1+i32
χ1911111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-111+i32−1−i321−i32−1+i32
χ2011111-1-1−1−i32−1+i32−1−i32−1+i32-111-1-11−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-11+i321+i321−i321−i321+i32−1−i321−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i321-1−1−i321+i32−1+i321−i32
χ2111111-1-1−1+i32−1−i32−1+i32−1−i321-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-111−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i32
χ2211111-1-1−1+i32−1−i32−1+i32−1−i321-11-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-111−i32−1+i321+i32−1−i32
χ2311111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i32
χ2411111-1-1−1+i32−1−i32−1+i32−1−i32-111-1-11−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-11−i321−i321+i321+i321−i32−1+i321+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i321-1−1+i321−i32−1−i321+i32
χ252222222222222222-1-1-1-1-1-1222222220000002222-1-1-1-1-1-1-1-1-1000000000-1-1-1-1-1-1000000
χ2622222222222-2-2222-1-1-1-1-1-1222222-2-2000000-2-2-2-2-1-1-1-1-1-1-1-1-1000000000111111000000
χ272222222−1−i3−1+i3−1−i3−1+i322222-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322000000−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000-1-11+i321+i321−i321−i32000000
χ282222222−1−i3−1+i3−1−i3−1+i3-2-2222-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-20000001+i31+i31−i31−i3-11+i321−i32-1-11+i321+i321−i321−i3200000000011−1−i32−1−i32−1+i32−1+i32000000
χ292222222−1+i3−1−i3−1+i3−1−i322222-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322000000−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000000-1-11−i321−i321+i321+i32000000
χ302222222−1+i3−1−i3−1+i3−1−i3-2-2222-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-20000001−i31−i31+i31+i3-11−i321+i32-1-11−i321−i321+i321+i3200000000011−1+i32−1+i32−1−i32−1−i32000000
χ3122222-2-222222-22-2-2-1-1-1-1-1-122-2-2-2-22-20000002-22-2-1-1-1111111000000000-11-11-11000000
χ3222222-2-22222-222-2-2-1-1-1-1-1-122-2-2-2-2-22000000-22-22-1-1-11111110000000001-11-11-1000000
χ3322222-2-2−1−i3−1+i3−1−i3−1+i32-22-2-2-11+i321−i32-11+i321−i32−1−i3−1+i31+i31+i31−i31−i32-2000000−1−i31+i3−1+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000-111+i32−1−i321−i32−1+i32000000
χ3422222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-11+i321−i32-11+i321−i32−1−i3−1+i31+i31+i31−i31−i3-220000001+i3−1−i31−i3−1+i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i320000000001-1−1−i321+i32−1+i321−i32000000
χ3522222-2-2−1+i3−1−i3−1+i3−1−i32-22-2-2-11−i321+i32-11−i321+i32−1+i3−1−i31−i31−i31+i31+i32-2000000−1+i31−i3−1−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000-111−i32−1+i321+i32−1−i32000000
χ3622222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-11−i321+i32-11−i321+i32−1+i3−1−i31−i31−i31+i31+i3-220000001−i3−1+i31+i3−1−i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i320000000001-1−1+i321−i32−1−i321+i32000000
χ37222-2200222200-200222222-2-20000002222220000-2-2-2000000-2-2-2000000000000000000
χ38222-2200222200-200222222-2-2000000-2-2-2-2-2-20000-2-2-2000000222000000000000000000
χ39222-2200−1−i3−1+i3−1−i3−1+i300-2002−1−i3−1+i32−1−i3−1+i31+i31−i300000022−1−i3−1−i3−1+i3−1+i30000-21+i31−i3000000-21+i31−i3000000000000000000
χ40222-2200−1−i3−1+i3−1−i3−1+i300-2002−1−i3−1+i32−1−i3−1+i31+i31−i3000000-2-21+i31+i31−i31−i30000-21+i31−i30000002−1−i3−1+i3000000000000000000
χ41222-2200−1+i3−1−i3−1+i3−1−i300-2002−1+i3−1−i32−1+i3−1−i31−i31+i300000022−1+i3−1+i3−1−i3−1−i30000-21−i31+i3000000-21−i31+i3000000000000000000
χ42222-2200−1+i3−1−i3−1+i3−1−i300-2002−1+i3−1−i32−1+i3−1−i31−i31+i3000000-2-21−i31−i31+i31+i30000-21−i31+i30000002−1+i3−1−i3000000000000000000
χ432-220-22−222-2-20002−2222-2-2-2002−22−2002i−2i2i−2i2i−2i00000002−22−22−2000−i2i2−i2i2−i2i2000000000000
χ442-220-22−222-2-20002−2222-2-2-2002−22−200−2i2i−2i2i−2i2i00000002−22−22−2000i2−i2i2−i2i2−i2000000000000
χ452-220-22−2−1−i3−1+i31+i31−i30002−22−1−i3−1+i3-21+i31−i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23002i−2i2ζ22−2ζ222ζ14−2ζ1400000002−2−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23000−i2i2ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23000000000000
χ462-220-22−2−1−i3−1+i31+i31−i30002−22−1−i3−1+i3-21+i31−i300−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300−2i2i−2ζ222ζ22−2ζ142ζ1400000002−2−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23000i2−i2−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23000000000000
χ472-220-22−2−1+i3−1−i31−i31+i30002−22−1+i3−1−i3-21−i31+i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13002i−2i2ζ14−2ζ142ζ22−2ζ2200000002−2ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13000−i2i2ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13000000000000
χ482-220-22−2−1+i3−1−i31−i31+i30002−22−1+i3−1−i3-21−i31+i300ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300−2i2i−2ζ142ζ14−2ζ222ζ2200000002−2ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13000i2−i2−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13000000000000
χ492-220-2−2222-2-2000−22222-2-2-200−22−22002i−2i2i−2i2i−2i0000000−22−22−22000i2−i2i2−i2i2−i2000000000000
χ502-220-2−2222-2-2000−22222-2-2-200−22−2200−2i2i−2i2i−2i2i0000000−22−22−22000−i2i2−i2i2−i2i2000000000000
χ512-220-2−22−1−i3−1+i31+i31−i3000−222−1−i3−1+i3-21+i31−i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23002i−2i2ζ22−2ζ222ζ14−2ζ140000000−22ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23000i2−i2−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23000000000000
χ522-220-2−22−1−i3−1+i31+i31−i3000−222−1−i3−1+i3-21+i31−i300ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300−2i2i−2ζ222ζ22−2ζ142ζ140000000−22ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23000−i2i2ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23000000000000
χ532-220-2−22−1+i3−1−i31−i31+i3000−222−1+i3−1−i3-21−i31+i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13002i−2i2ζ14−2ζ142ζ22−2ζ220000000−22−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13000i2−i2−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13000000000000
χ542-220-2−22−1+i3−1−i31−i31+i3000−222−1+i3−1−i3-21−i31+i300−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300−2i2i−2ζ142ζ14−2ζ222ζ220000000−22−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13000−i2i2ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13000000000000
χ55444-4400444400-400-2-2-2-2-2-2-4-40000000000000000222000000000000000000000000000
χ56444-4400−2−2i3−2+2i3−2−2i3−2+2i300-400-21+i31−i3-21+i31−i32+2i32−2i300000000000000002−1−i3−1+i3000000000000000000000000000
χ57444-4400−2+2i3−2−2i3−2+2i3−2−2i300-400-21−i31+i3-21−i31+i32−2i32+2i300000000000000002−1+i3−1−i3000000000000000000000000000
χ584-440-422−2244-4-400022−22-2-2-22220022−2222−22000000000000000−22−22−22000000000000000000000
χ594-440-422−22−2−2i3−2+2i32+2i32−2i300022−22-21+i31−i32−1−i3−1+i300−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ23000000000000000−22ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23000000000000000000000
χ604-440-422−22−2+2i3−2−2i32−2i32+2i300022−22-21−i31+i32−1+i3−1−i3002ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ13000000000000000−22−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13000000000000000000000
χ614-440-4−222244-4-4000−2222-2-2-222200−2222−22220000000000000002−22−22−2000000000000000000000
χ624-440-4−2222−2−2i3−2+2i32+2i32−2i3000−2222-21+i31−i32−1−i3−1+i3002ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ230000000000000002−2−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23000000000000000000000
χ634-440-4−2222−2+2i3−2−2i32−2i32+2i3000−2222-21−i31+i32−1+i3−1−i300−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ130000000000000002−2ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13000000000000000000000
χ6466-36-366000066-3-3-3000000000000-3-30000000000000000000000000000000000000000
χ6566-36-3660000-6-6-3-3-3000000000000330000000000000000000000000000000000000000
χ6666-36-3-6-600006-6-333000000000000-330000000000000000000000000000000000000000
χ6766-36-3-6-60000-66-3330000000000003-30000000000000000000000000000000000000000
χ681212-6-12-600000000600000000000000000000000000000000000000000000000000000000
χ6912-12-60662−620000000−3232000000000000000000000000000000000000000000000000000000
χ7012-12-606−6262000000032−32000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.