Finite Group Databasebeta

← Group #69115

Character table — Group #69115

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111222222222244444444446666888888888888888812121212121224242424
order12442346888812122468812242424248888612161616162424484848484848484844448816161616
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-11-1-1111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ611111111111111-1-11-1-1111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ711111111111111-1-11-1-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ811111111111111-1-11-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1
χ911111111-1-1-1-111111-1-11-1-1-1-1111111i−ii−i-1-1ii−i−iii−i−i-1-1-1-111i−ii−i
χ1011111111-1-1-1-111111-1-11-1-1-1-1111111−ii−ii-1-1−i−iii−i−iii-1-1-1-111−ii−ii
χ1111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111i−ii−i-1-1ii−i−iii−i−i1111-1-1−ii−ii
χ1211111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111−ii−ii-1-1−i−iii−i−iii1111-1-1i−ii−i
χ1311111111-1-1-1-111-1-11111-1-1-1-11111-1-1i−i−ii11ii−i−i−i−iii-1-111-1-1i−i−ii
χ1411111111-1-1-1-111-1-11111-1-1-1-11111-1-1−iii−i11−i−iiiii−i−i-1-111-1-1−iii−i
χ1511111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1i−i−ii11ii−i−i−i−iii11-1-111−iii−i
χ1611111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1−iii−i11−i−iiiii−i−i11-1-111i−i−ii
χ1722222-12-12222-1-122-122-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-10000000000
χ1822222-12-12222-1-122-122-1-1-1-1-10000-1-1-2-2-2-2-1-1111111110000000000
χ1922222-12-12222-1-1-2-2-1-2-2-1-1-1-1-100001122-2-211-1-1-1-111110000000000
χ2022222-12-12222-1-1-2-2-1-2-2-1-1-1-1-1000011-2-222111111-1-1-1-10000000000
χ2122222-12-1-2-2-2-2-1-122-1-2-2-111110000-1-12i−2i2i−2i11−i−iii−i−iii0000000000
χ2222222-12-1-2-2-2-2-1-122-1-2-2-111110000-1-1−2i2i−2i2i11ii−i−iii−i−i0000000000
χ2322222-12-1-2-2-2-2-1-1-2-2-122-111110000112i−2i−2i2i-1-1−i−iiiii−i−i0000000000
χ2422222-12-1-2-2-2-2-1-1-2-2-122-11111000011−2i2i2i−2i-1-1ii−i−i−i−iii0000000000
χ252222-22-2222-2-22200-200-222-2-200000000000000000000002i−2i2i−2i0000
χ262222-22-2222-2-22200-200-222-2-20000000000000000000000−2i2i−2i2i0000
χ272222-22-22-2-2222200-200-2-2-22200000000000000000000002i−2i−2i2i0000
χ282222-22-22-2-2222200-200-2-2-2220000000000000000000000−2i2i2i−2i0000
χ2922-2-222-222i−2i2i−2i-2-22-222i−2i-22i−2i2i−2i00002-200002i−2i000000000000000000
χ3022-2-222-222i−2i2i−2i-2-2-222−2i2i-22i−2i2i−2i0000-220000−2i2i000000000000000000
χ3122-2-222-22−2i2i−2i2i-2-22-22−2i2i-2−2i2i−2i2i00002-20000−2i2i000000000000000000
χ3222-2-222-22−2i2i−2i2i-2-2-2222i−2i-2−2i2i−2i2i0000-2200002i−2i000000000000000000
χ3322-2-22-1-2-12i−2i2i−2i112-2-12i−2i1−ii−ii0000-110000−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ3422-2-22-1-2-12i−2i2i−2i112-2-12i−2i1−ii−ii0000-110000−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ3522-2-22-1-2-12i−2i2i−2i11-22-1−2i2i1−ii−ii00001-10000i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ3622-2-22-1-2-12i−2i2i−2i11-22-1−2i2i1−ii−ii00001-10000i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ3722-2-22-1-2-1−2i2i−2i2i112-2-1−2i2i1i−ii−i0000-110000i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ3822-2-22-1-2-1−2i2i−2i2i112-2-1−2i2i1i−ii−i0000-110000i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ3922-2-22-1-2-1−2i2i−2i2i11-22-12i−2i1i−ii−i00001-10000−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4022-2-22-1-2-1−2i2i−2i2i11-22-12i−2i1i−ii−i00001-10000−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4122-2-2-22222i−2i−2i2i-2-200-20022i−2i−2i2i22-2-200000000000000002i−2i00000000
χ4222-2-2-22222i−2i−2i2i-2-200-20022i−2i−2i2i-2-2220000000000000000−2i2i00000000
χ4322-2-2-2222−2i2i2i−2i-2-200-2002−2i2i2i−2i22-2-20000000000000000−2i2i00000000
χ4422-2-2-2222−2i2i2i−2i-2-200-2002−2i2i2i−2i-2-22200000000000000002i−2i00000000
χ454444-4-2-4-244-4-4-2-2002002-2-222000000000000000000000000000000
χ464444-4-2-4-2-4-444-2-200200222-2-2000000000000000000000000000000
χ4744-4-4-4-24-24i−4i−4i4i2200200-2−2i2i2i−2i000000000000000000000000000000
χ4844-4-4-4-24-2−4i4i4i−4i2200200-22i−2i−2i2i000000000000000000000000000000
χ494-44i−4i040-400004i−4i000000000022−22−2i22i200000000000000000000000000
χ504-44i−4i040-400004i−4i0000000000−22222i2−2i200000000000000000000000000
χ514-4−4i4i040-40000−4i4i000000000022−222i2−2i200000000000000000000000000
χ524-4−4i4i040-40000−4i4i0000000000−2222−2i22i200000000000000000000000000
χ538-88i−8i0-4040000−4i4i0000000000000000000000000000000000000000
χ548-8−8i8i0-40400004i−4i0000000000000000000000000000000000000000

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