Finite Group Databasebeta

← Group #68519

Character table — Group #68519

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222222224444444444444444444466668888888888121212121212121212122424
order122244443444466612121212888888881212121224242424242424248888882424242424242424224488888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-1ii−i−ii−iii−i−iii−i−i11-1-1i−iii−i−i1-1
χ101111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-1−i−iiii−iii−i−iii−i−i-1-111−ii−i−iii-11
χ111111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111-1-111-1-1-1-11111ii−i−i−iiii−i−i−i−iii11-1-1i−i−i−iii-11
χ121111-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-111-1-111-1-1-1-11111−i−iii−iiii−i−i−i−iii-1-111−iiii−i−i1-1
χ131111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-1ii−i−i−ii−i−iii−i−iii-1-111i−iii−i−i-11
χ141111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-1−i−iii−ii−i−iii−i−iii11-1-1−ii−i−iii1-1
χ151111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111-1-111-1-1-1-11111ii−i−ii−i−i−iiiii−i−i-1-111i−i−i−iii1-1
χ161111-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-111-1-111-1-1-1-11111−i−iiii−i−i−iiiii−i−i11-1-1−iiii−i−i-11
χ17222222222-2-2-2-2222222200000000-2-2-2-200000000222200000000000000-2-2000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-2-2-20000000000000022000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000221111-1-1-1-1000000000000
χ232222-2-2-2-22-2-222222-2-2-2-20000000022-2-2000000002i2i−2i−2i00000000000000−2i2i000000
χ242222-2-2-2-22-2-222222-2-2-2-20000000022-2-200000000−2i−2i2i2i000000000000002i−2i000000
χ252222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i22-2-211-1-1-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ262222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i-2-22211-1-11111-1-1-1-10000−2i2i−i−iiiii−i−i000000000000
χ272222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i22-2-211-1-1-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ282222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i-2-22211-1-11111-1-1-1-100002i−2iii−i−i−i−iii000000000000
χ2922-2-222-2-2200002-2-222-2-20000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i22-22-20000000000000000−i2i2−i2i200
χ3022-2-222-2-2200002-2-222-2-20000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2-22-220000000000000000i2−i2i2−i200
χ3122-2-222-2-2200002-2-222-2-20000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i22-22-20000000000000000i2−i2i2−i200
χ3222-2-222-2-2200002-2-222-2-20000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2-22-220000000000000000−i2i2−i2i200
χ3322-2-2-2-222200002-2-2-2-2220000−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i00000000000000002−2−2200
χ3422-2-2-2-222200002-2-2-2-2220000−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0000000000000000−222−200
χ3522-2-2-2-222200002-2-2-2-2220000i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i0000000000000000−222−200
χ3622-2-2-2-222200002-2-2-2-2220000i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i00000000000000002−2−2200
χ372-22-22i−2i2i−2i22-22i−2i-22-22i−2i2i−2i000000002i−2i2-200000000000000000000002-22i−2i00000000
χ382-22-22i−2i2i−2i22-22i−2i-22-22i−2i2i−2i000000002i−2i2-20000000000000000000000-22−2i2i00000000
χ392-22-22i−2i2i−2i2-22−2i2i-22-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i-22000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ402-22-22i−2i2i−2i2-22−2i2i-22-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i-2200000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ412-22-22i−2i2i−2i-1-22−2i2i1-11−ii−ii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000i−i1-13−33−3−i3i3−i3i3000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ422-22-22i−2i2i−2i-1-22−2i2i1-11−ii−ii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000i−i1-1−33−33i3−i3i3−i3000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ432-22-22i−2i2i−2i-1-22−2i2i1-11−ii−ii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i−i1-13−33−3−i3i3−i3i3000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ442-22-22i−2i2i−2i-1-22−2i2i1-11−ii−ii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i−i1-1−33−33i3−i3i3−i3000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ452-22-2−2i2i−2i2i22-2−2i2i-22-2−2i2i−2i2i00000000−2i2i2-200000000000000000000002-2−2i2i00000000
χ462-22-2−2i2i−2i2i22-2−2i2i-22-2−2i2i−2i2i00000000−2i2i2-20000000000000000000000-222i−2i00000000
χ472-22-2−2i2i−2i2i2-222i−2i-22-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i-2200000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ482-22-2−2i2i−2i2i2-222i−2i-22-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i-22000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ492-22-2−2i2i−2i2i-1-222i−2i1-11i−ii−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−ii1-13−33−3i3−i3i3−i3000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ502-22-2−2i2i−2i2i-1-222i−2i1-11i−ii−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−ii1-1−33−33−i3i3−i3i3000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ512-22-2−2i2i−2i2i-1-222i−2i1-11i−ii−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ii1-13−33−3i3−i3i3−i3000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ522-22-2−2i2i−2i2i-1-222i−2i1-11i−ii−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ii1-1−33−33−i3i3−i3i3000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000
χ544444-4-4-4-4-2-4-444-2-2-2222200000000-2-2220000000000000000000000000000000000
χ5544-4-444-4-4-20000-222-2-2220000−2i22i2−2i22i20000i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ5644-4-444-4-4-20000-222-2-22200002i2−2i22i2−2i20000−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ5744-4-4-4-444-20000-22222-2-20000−2i22i22i2−2i20000i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ5844-4-4-4-444-20000-22222-2-200002i2−2i2−2i22i20000−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ594-44-44i−4i4i−4i-24-44i−4i2-22−2i2i−2i2i00000000−2i2i-220000000000000000000000000000000000
χ604-44-4−4i4i−4i4i-24-4−4i4i2-222i−2i2i−2i000000002i−2i-220000000000000000000000000000000000
χ614-4-444i−4i−4i4i40000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-4-444i−4i−4i4i-2000022-2−2i2i2i−2i000000000000i6−i6−i6i66−6−6600000000000000000000000000
χ634-4-444i−4i−4i4i-2000022-2−2i2i2i−2i000000000000−i6i6i6−i6−666−600000000000000000000000000
χ644-4-44−4i4i4i−4i40000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4-44−4i4i4i−4i-2000022-22i−2i−2i2i000000000000i6−i6−i6i6−666−600000000000000000000000000
χ664-4-44−4i4i4i−4i-2000022-22i−2i−2i2i000000000000−i6i6i6−i66−6−6600000000000000000000000000

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