Finite Group Databasebeta

← Group #11714005

Character table — Group #11714005

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1122222444446666888888881212121212121616161616161616161616164848484848484848
order12244882488822443612122424242424888866612121224242424242424448888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111-1-11-1-1111111111111-1-111-1-11-1-11-1-111-1-1-1-111-1-1-1-111
χ41111111-1-11-1-1111111111111-1-111-1-11-1-11-1-111-1-1-1-1-1-11111-1-1
χ511111-1-111-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-11-11-11-1
χ611111-1-111-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-11-11-11
χ711111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111-1-11-111-1
χ811111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-111-11-1-11
χ92222222222222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ102222222-2-22-2-22222-1-1-1-1-1-1-1-1-2-222-2-2-111-111-1-1111100000000
χ1122222-2-222-2-2-22222-1-1-1-1111122-2-2-2-2-1-1-1-1-1-111111100000000
χ1222222-2-2-2-2-2222222-1-1-1-11111-2-2-2-222-111-11111-1-1-1-100000000
χ13222-2-2000002i−2i-2-22222-2-2000000002i−2i200-200002i2i−2i−2i00000000
χ14222-2-2000002i−2i-2-222-1-11133−3−300002i−2i-1−i3i31−i3i33−3−i−iii00000000
χ15222-2-2000002i−2i-2-222-1-111−3−33300002i−2i-1i3−i31i3−i3−33−i−iii00000000
χ16222-2-200000−2i2i-2-22222-2-200000000−2i2i200-20000−2i−2i2i2i00000000
χ17222-2-200000−2i2i-2-222-1-11133−3−30000−2i2i-1i3−i31i3−i33−3ii−i−i00000000
χ18222-2-200000−2i2i-2-222-1-111−3−3330000−2i2i-1−i3i31−i3i3−33ii−i−i00000000
χ1922-22-22200-2002-2-2222222222002-200-200-200-2-2000000000000
χ2022-22-22200-2002-2-22-1-1-1-1-1-1-1-1002-2001−i3i31i3−i311−i3i3−i3i300000000
χ2122-22-22200-2002-2-22-1-1-1-1-1-1-1-1002-2001i3−i31−i3i311i3−i3i3−i300000000
χ2222-22-2-2-2002002-2-222222-2-2-2-200-2200-200-20022000000000000
χ2322-22-2-2-2002002-2-22-1-1-1-1111100-22001−i3i31i3−i3-1-1i3−i3i3−i300000000
χ2422-22-2-2-2002002-2-22-1-1-1-1111100-22001i3−i31−i3i3-1-1−i3i3−i3i300000000
χ2522-2-22002-2000-22-2222-2-20000-220000-2222-2-200000000000000
χ2622-2-22002-2000-22-22-1-11133−3−3-2200001-1-1-111−333−3−3300000000
χ2722-2-22002-2000-22-22-1-111−3−333-2200001-1-1-1113−3−333−300000000
χ2822-2-2200-22000-22-2222-2-200002-20000-2-2-222200000000000000
χ2922-2-2200-22000-22-22-1-11133−3−32-20000111-1-1-1−33−333−300000000
χ3022-2-2200-22000-22-22-1-111−3−3332-20000111-1-1-13−33−3−3300000000
χ31333333333333-1-1-1-100000000-1-1-1-1-1-100000000000011-1-111-1-1
χ32333333333333-1-1-1-100000000-1-1-1-1-1-1000000000000-1-111-1-111
χ333333333-3-33-3-3-1-1-1-10000000011-1-1110000000000001111-1-1-1-1
χ343333333-3-33-3-3-1-1-1-10000000011-1-111000000000000-1-1-1-11111
χ3533333-3-333-3-3-3-1-1-1-100000000-1-111110000000000001-1-111-1-11
χ3633333-3-333-3-3-3-1-1-1-100000000-1-11111000000000000-111-1-111-1
χ3733333-3-3-3-3-333-1-1-1-1000000001111-1-10000000000001-11-1-11-11
χ3833333-3-3-3-3-333-1-1-1-1000000001111-1-1000000000000-11-111-11-1
χ39666-6-6000006i−6i22-2-2000000000000−2i2i00000000000000000000
χ40666-6-600000−6i6i22-2-20000000000002i−2i00000000000000000000
χ4166-66-66600-600-222-20000000000-220000000000000000000000
χ4266-66-6-6-600600-222-200000000002-20000000000000000000000
χ4366-6-66006-60002-22-2000000002-2000000000000000000000000
χ4466-6-6600-660002-22-200000000-22000000000000000000000000
χ458-8000−4i24i20000000002-223−232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ468-8000−4i24i20000000002-2−23232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ478-8000−4i24i2000000000-4400−2i22i22i2−2i200000000000000000000000000
χ488-80004i2−4i20000000002-223−23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ498-80004i2−4i20000000002-2−2323−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ508-80004i2−4i2000000000-44002i2−2i2−2i22i200000000000000000000000000

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