Finite Group Databasebeta

← Group #69043

Character table — Group #69043

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111222222222244444488888888888888888812121212242424242424
order12442223444612126661212124488881212121224242424242424248888244488
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ611111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ92222222-1222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ102222222-1222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110000000000
χ112222222-1222-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111110000000000
χ122222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-10000000000
χ1322222-2-22-22-22222-2-22-2-22i−2i00002i2i−2i−2i000000000000000000
χ1422222-2-22-22-22222-2-22-2-2−2i2i0000−2i−2i2i2i000000000000000000
χ1522222-2-2-1-22-2-1-1-1-111-1112i−2i0000−i−iii−i3−i3i3i333−3−30000000000
χ1622222-2-2-1-22-2-1-1-1-111-1112i−2i0000−i−iiii3i3−i3−i3−3−3330000000000
χ1722222-2-2-1-22-2-1-1-1-111-111−2i2i0000ii−i−i−i3−i3i3i3−3−3330000000000
χ1822222-2-2-1-22-2-1-1-1-111-111−2i2i0000ii−i−ii3i3−i3−i333−3−30000000000
χ192222-22-222-2-2222-2-22-22-2000000000000000000000000002i−2i
χ202222-22-222-2-2222-2-22-22-200000000000000000000000000−2i2i
χ212222-2-222-2-22222-22-2-2-220000000000000000000000002-200
χ222222-2-222-2-22222-22-2-2-22000000000000000000000000-2200
χ2322-2-22222-2-2-22-2-2222-2-2-200002i−2i000000002i−2i2i−2i0000000000
χ2422-2-22222-2-2-22-2-2222-2-2-20000−2i2i00000000−2i2i−2i2i0000000000
χ2522-2-2222-1-2-2-2-111-1-1-111100002i−2i−i3i3−i3i33−33−3−ii−ii0000000000
χ2622-2-2222-1-2-2-2-111-1-1-111100002i−2ii3−i3i3−i3−33−33−ii−ii0000000000
χ2722-2-2222-1-2-2-2-111-1-1-11110000−2i2i−i3i3−i3i3−33−33i−ii−i0000000000
χ2822-2-2222-1-2-2-2-111-1-1-11110000−2i2ii3−i3i3−i33−33−3i−ii−i0000000000
χ2922-2-22-2-222-222-2-22-2-2-222002i−2i0000002i−2i−2i2i00000000000000
χ3022-2-22-2-222-222-2-22-2-2-22200−2i2i000000−2i2i2i−2i00000000000000
χ3122-2-22-2-2-12-22-111-1111-1-1002i−2i003−3−33−iii−ii3−i3−i3i30000000000
χ3222-2-22-2-2-12-22-111-1111-1-1002i−2i00−333−3−iii−i−i3i3i3−i30000000000
χ3322-2-22-2-2-12-22-111-1111-1-100−2i2i003−3−33i−i−ii−i3i3i3−i30000000000
χ3422-2-22-2-2-12-22-111-1111-1-100−2i2i00−333−3i−i−iii3−i3−i3i30000000000
χ3522-2-2-22-22-2222-2-2-2-222-2200000000000000000000002-20000
χ3622-2-2-22-22-2222-2-2-2-222-220000000000000000000000-220000
χ3722-2-2-2-22222-22-2-2-22-222-20000000000000000002i2i−2i−2i000000
χ3822-2-2-2-22222-22-2-2-22-222-2000000000000000000−2i−2i2i2i000000
χ394444-44-4-24-4-4-2-2-222-22-220000000000000000000000000000
χ404444-4-44-2-4-44-2-2-22-2222-20000000000000000000000000000
χ4144-4-4-44-4-2-444-22222-2-22-20000000000000000000000000000
χ4244-4-4-4-44-244-4-2222-22-2-220000000000000000000000000000
χ434-44i−4i0004000-44i−4i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ444-44i−4i0004000-44i−4i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ454-4−4i4i0004000-4−4i4i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ464-4−4i4i0004000-4−4i4i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ478-88i−8i000-40004−4i4i0000000000000000000000000000000000
χ488-8−8i8i000-400044i−4i0000000000000000000000000000000000

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