Finite Group Databasebeta

← Group #71801

Character table — Group #71801

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order122244443444444446661212121224661212121212121212121222446666121212128888888888888888
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
χ511111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-11-1-1111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-11-1-1111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-111-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-111-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111-1-111-1-1111-1-1-1-1-11-1-111-1-1-1-1111111-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1111-1-111-1-1111-1-1-1-1-11-1-111-1-1-1-1111111-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1111-1-111-1-1111-1-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1111-1-111-1-1111-1-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ17222222222-2-22222-2-22222222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222222-122-2-2-2-222-1-1-1-1-1-1-1-2-211-1-1-1-11111112-22-2-1-111-1-1110000000000000000
χ2222222222-122-2-2-2-222-1-1-1-1-1-1-1-2-211-1-1-1-1111111-22-2211-1-111-1-10000000000000000
χ2322222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2111111-1-1-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2422222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2111111-1-1-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-111111111-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-111111111-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ272222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-22222-2-2220000000000000000000000000000
χ282222-2-2-2-22-2-2-2-22222222-2-2-2-22-222-2-222-2-222-2-20000000000000000000000000000
χ292222-2-2-2-2-12222-2-2-2-2-1-1-111112-2-1-1-1-111-1-111112-2-22-1-11111-1-10000000000000000
χ302222-2-2-2-2-12222-2-2-2-2-1-1-111112-2-1-1-1-111-1-11111-222-211-1-1-1-1110000000000000000
χ312222-2-2-2-2-122-2-222-2-2-1-1-11111-2211-1-11111-1-1-1-122-2-2-1-1-1-111110000000000000000
χ322222-2-2-2-2-122-2-222-2-2-1-1-11111-2211-1-11111-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ332222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-111-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ342222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-111-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ352222-2-2-2-2-1-2-2-2-22222-1-1-111112-2-1-111-1-111-1-1110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ362222-2-2-2-2-1-2-2-2-22222-1-1-111112-2-1-111-1-111-1-1110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ3722-2-22i2i−2i−2i2002i−2i2-2002-2-22i2i−2i−2i000000002i−2i2-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3822-2-22i2i−2i−2i2002i−2i2-2002-2-22i2i−2i−2i000000002i−2i2-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3922-2-22i2i−2i−2i200−2i2i-22002-2-22i2i−2i−2i00000000−2i2i-2200000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ4022-2-22i2i−2i−2i200−2i2i-22002-2-22i2i−2i−2i00000000−2i2i-220000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ4122-2-2−2i−2i2i2i2002i−2i-22002-2-2−2i−2i2i2i000000002i−2i-2200000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ4222-2-2−2i−2i2i2i2002i−2i-22002-2-2−2i−2i2i2i000000002i−2i-220000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ4322-2-2−2i−2i2i2i200−2i2i2-2002-2-2−2i−2i2i2i00000000−2i2i2-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ4422-2-2−2i−2i2i2i200−2i2i2-2002-2-2−2i−2i2i2i00000000−2i2i2-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ452-22-22i−2i2i−2i22-200002i−2i-22-22i−2i2i−2i00002-22i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ462-22-22i−2i2i−2i22-200002i−2i-22-22i−2i2i−2i00002-22i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ472-22-22i−2i2i−2i2-220000−2i2i-22-22i−2i2i−2i0000-22−2i2i0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ482-22-22i−2i2i−2i2-220000−2i2i-22-22i−2i2i−2i0000-22−2i2i000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ492-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i2i−2i2i00002-2−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ502-22-2−2i2i−2i2i22-20000−2i2i-22-2−2i2i−2i2i00002-2−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ512-22-2−2i2i−2i2i2-2200002i−2i-22-2−2i2i−2i2i0000-222i−2i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ522-22-2−2i2i−2i2i2-2200002i−2i-22-2−2i2i−2i2i0000-222i−2i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5344-4-44i4i−4i−4i-2004i−4i4-400-222−2i−2i2i2i00000000−2i2i-22000000000000000000000000000000
χ5444-4-44i4i−4i−4i-200−4i4i-4400-222−2i−2i2i2i000000002i−2i2-2000000000000000000000000000000
χ5544-4-4−4i−4i4i4i-2004i−4i-4400-2222i2i−2i−2i00000000−2i2i2-2000000000000000000000000000000
χ5644-4-4−4i−4i4i4i-200−4i4i4-400-2222i2i−2i−2i000000002i−2i-22000000000000000000000000000000
χ574-44-44i−4i4i−4i-24-400004i−4i2-22−2i2i−2i2i0000-22−2i2i0000000000000000000000000000000000
χ584-44-44i−4i4i−4i-2-440000−4i4i2-22−2i2i−2i2i00002-22i−2i0000000000000000000000000000000000
χ594-44-4−4i4i−4i4i-24-40000−4i4i2-222i−2i2i−2i0000-222i−2i0000000000000000000000000000000000
χ604-44-4−4i4i−4i4i-2-4400004i−4i2-222i−2i2i−2i00002-2−2i2i0000000000000000000000000000000000
χ614-4-444-4-44400000000-4-444-4-44000000000000000000000000000000000000000000
χ624-4-444-4-44-20000000022-2-222-200−2i32i300000000−2i32i30000000000000000000000000000
χ634-4-444-4-44-20000000022-2-222-2002i3−2i3000000002i3−2i30000000000000000000000000000
χ644-4-44-444-4400000000-4-44-444-4000000000000000000000000000000000000000000
χ654-4-44-444-4-20000000022-22-2-2200−2i32i3000000002i3−2i30000000000000000000000000000
χ664-4-44-444-4-20000000022-22-2-22002i3−2i300000000−2i32i30000000000000000000000000000

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