Finite Group Databasebeta

← Group #68698

Character table — Group #68698

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111222222222244444488888888888888888812121212242424242424
order12442223444612126661212124444881212121212121212242424248888224444
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ511111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1
χ611111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
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
χ1322222-2-222-2-2222-22-22-2-2002i−2i0000002i2i−2i−2i00000000000000
χ1422222-2-222-2-2222-22-22-2-200−2i2i000000−2i−2i2i2i00000000000000
χ1522222-2-2-12-2-2-1-1-11-11-111002i−2i00−i3−i3i3i3−i−iii33−3−30000000000
χ1622222-2-2-12-2-2-1-1-11-11-111002i−2i00i3i3−i3−i3−i−iii−3−3330000000000
χ1722222-2-2-12-2-2-1-1-11-11-11100−2i2i00−i3−i3i3i3ii−i−i−3−3330000000000
χ1822222-2-2-12-2-2-1-1-11-11-11100−2i2i00i3i3−i3−i3ii−i−i33−3−30000000000
χ192222-22-22-22-2222-2-22-22-22i−2i00002i−2i2i−2i000000000000000000
χ202222-22-22-22-2222-2-22-22-2−2i2i0000−2i2i−2i2i000000000000000000
χ212222-22-2-1-22-2-1-1-111-11-112i−2i0000−ii−ii−i3i3−i3i33−33−30000000000
χ222222-22-2-1-22-2-1-1-111-11-112i−2i0000−ii−iii3−i3i3−i3−33−330000000000
χ232222-22-2-1-22-2-1-1-111-11-11−2i2i0000i−ii−i−i3i3−i3i3−33−330000000000
χ242222-22-2-1-22-2-1-1-111-11-11−2i2i0000i−ii−ii3−i3i3−i33−33−30000000000
χ252222-2-222-2-222222-2-2-2-2200002-2000000002-2-220000000000
χ262222-2-222-2-222222-2-2-2-220000-2200000000-222-20000000000
χ272222-2-22-1-2-22-1-1-1-11111-100002-23−3−33−333−3-111-10000000000
χ282222-2-22-1-2-22-1-1-1-11111-100002-2−333−33−3−33-111-10000000000
χ292222-2-22-1-2-22-1-1-1-11111-10000-223−3−333−3−331-1-110000000000
χ302222-2-22-1-2-22-1-1-1-11111-10000-22−333−3−333−31-1-110000000000
χ3122-2-22222-2-2-22-2-2222-2-2-2000000000000000000000000002-2
χ3222-2-22222-2-2-22-2-2222-2-2-200000000000000000000000000-22
χ3322-2-22-2-22-2222-2-2-22-2-222000000000000000000000020-2000
χ3422-2-22-2-22-2222-2-2-22-2-2220000000000000000000000-202000
χ3522-2-2-22-222-222-2-2-2-222-220000000000000000000000020-200
χ3622-2-2-22-222-222-2-2-2-222-2200000000000000000000000-20200
χ3722-2-2-2-22222-22-2-22-2-222-20000000000000000002i2i−2i−2i000000
χ3822-2-2-2-22222-22-2-22-2-222-2000000000000000000−2i−2i2i2i000000
χ3944-4-4444-2-4-4-4-222-2-2-22220000000000000000000000000000
χ4044-4-44-4-4-2-444-2222-222-2-20000000000000000000000000000
χ4144-4-4-44-4-24-44-22222-2-22-20000000000000000000000000000
χ4244-4-4-4-44-244-4-222-222-2-220000000000000000000000000000
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.