Finite Group Databasebeta

← Group #70413

Character table — Group #70413

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222444444444488888888888888881212121212121212121212122424
order124422234446121222446661212124466881212121212122424242422224444888844
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ611111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ811111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ911-1-11-1-1111-11-1-11-11-11-1-111-1i−i1-1i−i1-1ii−i−iii−i−i1-1111-1-1-1ii−i−ii−i
χ1011-1-11-1-1111-11-1-11-11-11-1-111-1i−i1-1i−i1-1ii−i−iii−i−i-11-1-1-1111−i−iii−ii
χ1111-1-11-1-1111-11-1-11-11-11-1-111-1−ii1-1−ii1-1−i−iii−i−iii1-1111-1-1-1−i−iii−ii
χ1211-1-11-1-1111-11-1-11-11-11-1-111-1−ii1-1−ii1-1−i−iii−i−iii-11-1-1-1111ii−i−ii−i
χ1311-1-11-1-1111-11-1-1-11-111-1-111-1i−i-11−ii-11ii−i−i−i−iii1-1-1-11-111ii−i−i−ii
χ1411-1-11-1-1111-11-1-1-11-111-1-111-1i−i-11−ii-11ii−i−i−i−iii-1111-11-1-1−i−iiii−i
χ1511-1-11-1-1111-11-1-1-11-111-1-111-1−ii-11i−i-11−i−iiiii−i−i1-1-1-11-111−i−iiii−i
χ1611-1-11-1-1111-11-1-1-11-111-1-111-1−ii-11i−i-11−i−iiiii−i−i-1111-11-1-1ii−i−i−ii
χ172222222-1222-1-1-12222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-1-2-2-1-1-2-2-1-11111111100000000000000
χ192222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-12211-2-211-1-1-1-1111100000000000000
χ202222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-21122111111-1-1-1-100000000000000
χ2122222-2-22-2-2222200002-2-2-2-220000000000000000002-2002-2000000
χ2222222-2-22-2-2222200002-2-2-2-22000000000000000000-2200-22000000
χ232222-22-222-2-22222-2-22-2-222-2-2002-200-220000000000000000000000
χ242222-22-222-2-2222-222-2-2-222-2-200-22002-20000000000000000000000
χ252222-22-2-12-2-2-1-1-12-2-2211-1-11100-11001-1−i3i3−i3i3−i3i3−i3i300000000000000
χ262222-22-2-12-2-2-1-1-12-2-2211-1-11100-11001-1i3−i3i3−i3i3−i3i3−i300000000000000
χ272222-22-2-12-2-2-1-1-1-222-211-1-111001-100-11−i3i3−i3i3i3−i3i3−i300000000000000
χ282222-22-2-12-2-2-1-1-1-222-211-1-111001-100-11i3−i3i3−i3−i3i3−i3i300000000000000
χ292222-2-222-22-22220000-22-2-22-200000000000000002-200-2200000000
χ302222-2-222-22-22220000-22-2-22-20000000000000000-22002-200000000
χ3122-2-22222-2-2-22-2-20000222-2-2-20000000000000000002-200-22000000
χ3222-2-22222-2-2-22-2-20000222-2-2-2000000000000000000-22002-2000000
χ3322-2-22-2-2-122-2-1112-22-2-111-1-112i−2i-112i−2i-11−i−iii−i−iii00000000000000
χ3422-2-22-2-2-122-2-1112-22-2-111-1-11−2i2i-11−2i2i-11ii−i−iii−i−i00000000000000
χ3522-2-22-2-2-122-2-111-22-22-111-1-112i−2i1-1−2i2i1-1−i−iiiii−i−i00000000000000
χ3622-2-22-2-2-122-2-111-22-22-111-1-11−2i2i1-12i−2i1-1ii−i−i−i−iii00000000000000
χ3722-2-2-22-22-2222-2-20000-2-22-22200000000000000002200-2-200000000
χ3822-2-2-22-22-2222-2-20000-2-22-2220000000000000000-2-2002200000000
χ3922-2-2-2-2222-222-2-222-2-2-22-22-22002200-2-20000000000000000000000
χ4022-2-2-2-2222-222-2-2-2-222-22-22-2200-2-200220000000000000000000000
χ4122-2-2-2-22-12-22-11122-2-21-11-11-100-1-100113−3−333−3−3300000000000000
χ4222-2-2-2-22-12-22-11122-2-21-11-11-100-1-10011−333−3−333−300000000000000
χ4322-2-2-2-22-12-22-111-2-2221-11-11-1001100-1-13−3−33−333−300000000000000
χ4422-2-2-2-22-12-22-111-2-2221-11-11-1001100-1-1−333−33−3−3300000000000000
χ4544444-4-4-2-4-44-2-2-20000-22222-2000000000000000000000000000000
χ464444-4-44-2-44-4-2-2-200002-222-22000000000000000000000000000000
χ4744-4-4444-2-4-4-4-2220000-2-2-2222000000000000000000000000000000
χ4844-4-4-44-4-2-444-222000022-22-2-2000000000000000000000000000000
χ494-44i−4i0004000-44i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ504-44i−4i0004000-44i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ514-4−4i4i0004000-4−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ524-4−4i4i0004000-4−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ538-88i−8i000-40004−4i4i0000000000000000000000000000000000000000
χ548-8−8i8i000-400044i−4i0000000000000000000000000000000000000000

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