Finite Group Databasebeta

← Group #71824

Character table — Group #71824

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222444422344444466612121212446612121212121212121212444412121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-11-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-11-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111-1-11-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111-1-11-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-111-1-1111-1-1-1-11-111-1-111-1-111-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1-111-1-1111-1-1-1-11-111-1-111-1-111-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1-111-1-1111-1-1-1-11-111-1-111-1-111-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-111-1-1111-1-1-1-11-111-1-111-1-111-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-1111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-1111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ202222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ212222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2222222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ2422222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ2522222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-2-2220000000000000000000000000000
χ282222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-111-1-111-1-1112-22-2-1-111-1-1110000000000000000
χ292222-2-2-2-222-1-2-222-2-2-1-1-111112-2-1-111-1-111-1-111-22-2211-1-111-1-10000000000000000
χ302222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-111-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ312222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-111-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ322222-2-2-2-2-2-2222-2-222222-2-2-2-22-2-2-222-2-22222-2-20000000000000000000000000000
χ332222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-11111-1-12-2-22-1-11111-1-10000000000000000
χ342222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-11111-1-1-222-211-1-1-1-1110000000000000000
χ352222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-111-1-1-1-1110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ362222-2-2-2-2-2-2-122-2-222-1-1-111112-211-1-111-1-1-1-1110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3722-2-222-2-22-222-200002-2-222-2-2002-22-200000000000000000000000000002−22−22−22−2
χ3822-2-222-2-22-222-200002-2-222-2-2002-22-20000000000000000000000000000−22−22−22−22
χ3922-2-222-2-2-222-2200002-2-222-2-200-22-2200000000000000000000000000002−22−2−22−22
χ4022-2-222-2-2-222-2200002-2-222-2-200-22-220000000000000000000000000000−22−222−22−2
χ4122-2-2-2-2222-22-2200002-2-2-2-222002-2-220000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4222-2-2-2-2222-22-2200002-2-2-2-222002-2-220000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4322-2-2-2-222-2222-200002-2-2-2-22200-222-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ4422-2-2-2-222-2222-200002-2-2-2-22200-222-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ452-22-22i−2i2i−2i002002-22i−2i-22-22i−2i2i−2i0000002-22i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ462-22-22i−2i2i−2i002002-22i−2i-22-22i−2i2i−2i0000002-22i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ472-22-22i−2i2i−2i00200-22−2i2i-22-22i−2i2i−2i000000-22−2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ482-22-22i−2i2i−2i00200-22−2i2i-22-22i−2i2i−2i000000-22−2i2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ492-22-2−2i2i−2i2i002002-2−2i2i-22-2−2i2i−2i2i0000002-2−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ502-22-2−2i2i−2i2i002002-2−2i2i-22-2−2i2i−2i2i0000002-2−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ512-22-2−2i2i−2i2i00200-222i−2i-22-2−2i2i−2i2i000000-222i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ522-22-2−2i2i−2i2i00200-222i−2i-22-2−2i2i−2i2i000000-222i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5344-4-444-4-44-4-24-40000-222-2-22200-22-22000000000000000000000000000000000000
χ5444-4-444-4-4-44-2-440000-222-2-222002-22-2000000000000000000000000000000000000
χ5544-4-4-4-4444-4-2-440000-22222-2-200-222-2000000000000000000000000000000000000
χ5644-4-4-4-444-44-24-40000-22222-2-2002-2-22000000000000000000000000000000000000
χ574-44-44i−4i4i−4i00-2004-44i−4i2-22−2i2i−2i2i000000-22−2i2i00000000000000000000000000000000
χ584-44-44i−4i4i−4i00-200-44−4i4i2-22−2i2i−2i2i0000002-22i−2i00000000000000000000000000000000
χ594-44-4−4i4i−4i4i00-2004-4−4i4i2-222i−2i2i−2i000000-222i−2i00000000000000000000000000000000
χ604-44-4−4i4i−4i4i00-200-444i−4i2-222i−2i2i−2i0000002-2−2i2i00000000000000000000000000000000
χ614-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i000000000023−23−2i32i30000000000000000000000000000
χ634-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i0000000000−23232i3−2i30000000000000000000000000000
χ644-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i000000000023−232i3−2i30000000000000000000000000000
χ664-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i0000000000−2323−2i32i30000000000000000000000000000

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